All 7 Uses

solemn
in
Alice's Adventures in Wonderland
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'In that case,' said the Dodo solemnly, rising to its feet, 'I move that the meeting adjourn, for the immediate adoption of more energetic remedies—' 'Speak English!' said the Eaglet.†
Chpt 3

solemnly = with seriousness and dignity
Then they all crowded round her once more, while the Dodo solemnly presented the thimble, saying 'We beg your acceptance of this elegant thimble'; and, when it had finished this short speech, they all cheered.†
Chpt 3
Alice thought the whole thing very absurd, but they all looked so grave that she did not dare to laugh; and, as she could not think of anything to say, she simply bowed, and took the thimble, looking as solemn as she could.†
Chpt 3

solemn = very serious--possibly dignified
The Fish-Footman began by producing from under his arm a great letter, nearly as large as himself, and this he handed over to the other, saying, in a solemn tone, 'For the Duchess.†
Chpt 6
The Frog-Footman repeated, in the same solemn tone, only changing the order of the words a little, 'From the Queen.†
Chpt 6
So they began solemnly dancing round and round Alice, every now and then treading on her toes when they passed too close, and waving their forepaws to mark the time, while the Mock Turtle sang this, very slowly and sadly:— '"Will you walk a little faster?" said a whiting to a snail.†
Chpt 10

solemnly = with seriousness and dignity
the Gryphon replied very solemnly.
Chpt 10 *

Definitions:

(1) (solemn)
in a very serious (and often dignified) manner
(2) (meaning too rare to warrant focus)
Less commonly, solemn can mean that something was done with great or appropriate ceremony. It can also be used to describe something as dark or undecorated.