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Properties

Label 23.13
Level 23
Weight 13
Dimension 253
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 572
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 13 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(572\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(23))\).

Total New Old
Modular forms 275 275 0
Cusp forms 253 253 0
Eisenstein series 22 22 0

Trace form

\( 253 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} + O(q^{10}) \) \( 253 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} - 11 q^{10} - 11 q^{11} - 11 q^{12} - 11 q^{13} - 11 q^{14} - 62475963 q^{15} + 95293429 q^{16} - 80926571 q^{17} + 153021429 q^{18} + 111165109 q^{19} - 272498699 q^{20} - 600623771 q^{21} + 648695509 q^{23} + 1642967018 q^{24} - 554361995 q^{25} - 1437765131 q^{26} - 721348331 q^{27} + 3957719029 q^{28} + 1286152549 q^{29} - 3340699659 q^{30} - 2846329211 q^{31} + 3825930229 q^{32} + 3117947349 q^{33} - 13971708113 q^{34} + 5952374989 q^{35} + 20606624764 q^{36} - 17898788171 q^{37} - 26779027286 q^{38} + 7541580805 q^{39} + 61210874989 q^{40} + 10673506789 q^{41} - 31821396761 q^{42} - 41404506011 q^{43} - 66452112342 q^{44} + 95430895549 q^{46} + 68725348538 q^{47} + 79448678573 q^{48} - 44826881627 q^{49} - 169189453136 q^{50} - 105406226651 q^{51} - 69154458461 q^{52} + 51469276309 q^{53} + 243641488893 q^{54} + 72464970853 q^{55} + 293616662416 q^{56} - 250324213931 q^{57} - 368388880706 q^{58} - 8207384339 q^{59} - 233131567141 q^{60} + 210924022837 q^{61} + 514816473589 q^{62} + 295298022789 q^{63} - 85261811723 q^{64} - 572376553067 q^{65} - 898520009904 q^{66} - 163067150411 q^{67} + 473498556069 q^{69} + 1235346917354 q^{70} + 712219883749 q^{71} + 629768899738 q^{72} - 166826901131 q^{73} - 311901254588 q^{74} - 4023714628043 q^{75} - 845476021610 q^{76} + 1996690386229 q^{77} + 3635414304819 q^{78} + 686225579413 q^{79} - 1205174134802 q^{80} - 4033886494363 q^{81} - 2043383696321 q^{82} - 415316705771 q^{83} + 7244741619995 q^{84} + 5849039441773 q^{85} - 200733189437 q^{86} - 3275269203371 q^{87} - 4135942853955 q^{88} - 3344097505331 q^{89} - 6933278864446 q^{90} + 3671001058714 q^{92} + 8439971139578 q^{93} + 6825771102128 q^{94} + 5731295760421 q^{95} - 7988018650040 q^{96} - 2782724911571 q^{97} - 1436224802771 q^{98} - 7415031217451 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(23))\)

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
23.13.b \(\chi_{23}(22, \cdot)\) 23.13.b.a 1 1
23.13.b.b 2
23.13.b.c 20
23.13.d \(\chi_{23}(5, \cdot)\) 23.13.d.a 230 10