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Properties

Label 23.10
Level 23
Weight 10
Dimension 187
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 440
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(440\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(23))\).

Total New Old
Modular forms 209 207 2
Cusp forms 187 187 0
Eisenstein series 22 20 2

Trace form

\( 187 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} + O(q^{10}) \) \( 187 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} - 11 q^{10} - 11 q^{11} - 11 q^{12} - 11 q^{13} - 11 q^{14} + 969023 q^{15} - 478731 q^{16} - 1054867 q^{17} + 1519925 q^{18} + 1526459 q^{19} + 3198965 q^{20} - 3575231 q^{21} - 5153654 q^{22} - 3650823 q^{23} + 6167018 q^{24} + 8299797 q^{25} + 9664149 q^{26} + 3875311 q^{27} - 21469195 q^{28} - 10200751 q^{29} - 24330955 q^{30} + 9969839 q^{31} + 46627317 q^{32} - 21902947 q^{33} - 8377589 q^{34} + 57736239 q^{35} - 30672686 q^{36} - 107778935 q^{37} - 92052576 q^{38} + 23347753 q^{39} + 213344989 q^{40} + 62844639 q^{41} + 178280179 q^{42} - 29184023 q^{43} - 225229796 q^{44} - 270641272 q^{45} - 311125331 q^{46} - 54389346 q^{47} + 183376413 q^{48} + 341786995 q^{49} + 511328114 q^{50} + 237700969 q^{51} + 138729679 q^{52} - 103750977 q^{53} - 1104475251 q^{54} - 96640643 q^{55} + 210507990 q^{56} + 59318281 q^{57} + 513967300 q^{58} - 118047545 q^{59} - 1153719721 q^{60} + 344711653 q^{61} + 980989141 q^{62} + 882717759 q^{63} + 986185717 q^{64} + 158418557 q^{65} - 747426636 q^{66} - 378627887 q^{67} - 2822341654 q^{68} - 1069913031 q^{69} - 1006270870 q^{70} + 56718519 q^{71} + 1971614260 q^{72} + 582788437 q^{73} + 699926392 q^{74} + 3594630963 q^{75} + 4934994042 q^{76} + 832730437 q^{77} - 4315286437 q^{78} - 4249645807 q^{79} - 10615143550 q^{80} - 5321334799 q^{81} + 416976439 q^{82} + 3425248739 q^{83} + 14370912435 q^{84} + 7253042687 q^{85} + 779636011 q^{86} + 2829378673 q^{87} - 671992739 q^{88} - 2402723741 q^{89} - 12214147682 q^{90} - 6034596590 q^{91} - 6333894578 q^{92} - 5895816058 q^{93} - 1344916188 q^{94} - 1504040945 q^{95} + 17191683300 q^{96} + 11525413603 q^{97} + 12597404941 q^{98} + 10210410199 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(23))\)

We only show spaces with even 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
23.10.a \(\chi_{23}(1, \cdot)\) 23.10.a.a 7 1
23.10.a.b 10
23.10.c \(\chi_{23}(2, \cdot)\) 23.10.c.a 170 10