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Properties

Label 23.19
Level 23
Weight 19
Dimension 385
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 836
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 19 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(836\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(\Gamma_1(23))\).

Total New Old
Modular forms 407 407 0
Cusp forms 385 385 0
Eisenstein series 22 22 0

Trace form

\( 385 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} + O(q^{10}) \) \( 385 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} - 11 q^{10} - 11 q^{11} - 11 q^{12} - 11 q^{13} - 11 q^{14} + 253448904621 q^{15} + 244859535349 q^{16} - 296340696091 q^{17} + 1295617765365 q^{18} + 34950057109 q^{19} - 4104516534283 q^{20} + 5306405877949 q^{21} - 7913631520443 q^{23} + 19270371901418 q^{24} + 12606229779253 q^{25} - 21033541703691 q^{26} - 20997579686171 q^{27} + 105657239863285 q^{28} - 6541999781251 q^{29} - 190975720579083 q^{30} + 83672683954189 q^{31} - 180361965076491 q^{32} + 261034241184453 q^{33} - 129972082436273 q^{34} - 364099226562511 q^{35} + 603126531762964 q^{36} + 428874756612181 q^{37} - 1776255039233686 q^{38} + 660838707811645 q^{39} + 3407519671874989 q^{40} - 634216393005811 q^{41} - 6199000632151481 q^{42} + 1284249744062989 q^{43} + 7033574851458386 q^{44} - 11646585269672771 q^{46} - 3522887998322990 q^{47} + 12458821923919085 q^{48} + 14035963270346413 q^{49} - 4993438720703136 q^{50} - 15827415309093971 q^{51} - 14461678566782381 q^{52} + 10327001802201029 q^{53} + 12987191024741373 q^{54} - 14661855368904755 q^{55} - 112789689088256488 q^{56} + 79316406647596261 q^{57} + 62208472164707374 q^{58} - 117859066247350879 q^{59} + 56789760614471819 q^{60} + 64312558011025621 q^{61} + 83888698739788789 q^{62} - 56271156969207411 q^{63} - 201906206426529803 q^{64} - 45304722356970395 q^{65} + 206405045580983832 q^{66} + 65297330513632789 q^{67} - 207859220028632931 q^{69} - 356233436672864278 q^{70} + 24270067030568029 q^{71} + 756779185849811410 q^{72} + 127844244594538549 q^{73} + 102815849039067692 q^{74} + 26566279111019989 q^{75} - 930398829208773122 q^{76} - 443460150706078891 q^{77} + 2393428849655474499 q^{78} + 960132297145477093 q^{79} - 2513912900105850122 q^{80} - 3427352266319555299 q^{81} + 340169380251389359 q^{82} + 2134251156441149669 q^{83} + 1875963344476894475 q^{84} - 2007915736107785735 q^{85} - 709961756623859245 q^{86} - 2814685211205824891 q^{87} + 746914657235259645 q^{88} + 2323216414828777369 q^{89} + 6947866797842083322 q^{90} - 3937280132812101086 q^{92} - 6843946090804105822 q^{93} - 2005788328569711400 q^{94} + 651951644569950461 q^{95} + 21994075423362001696 q^{96} + 2956262222729055625 q^{97} - 7668098686336153747 q^{98} - 9593810550169008251 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{19}^{\mathrm{new}}(\Gamma_1(23))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
23.19.b \(\chi_{23}(22, \cdot)\) 23.19.b.a 1 1
23.19.b.b 2
23.19.b.c 32
23.19.d \(\chi_{23}(5, \cdot)\) 23.19.d.a 350 10