Properties

Label 23.6
Level 23
Weight 6
Dimension 99
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 264
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(264\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(23))\).

Total New Old
Modular forms 121 119 2
Cusp forms 99 99 0
Eisenstein series 22 20 2

Trace form

\( 99 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} + O(q^{10}) \) \( 99 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} - 11 q^{10} - 11 q^{11} - 11 q^{12} - 11 q^{13} - 11 q^{14} - 4642 q^{15} + 3861 q^{16} + 3960 q^{17} + 12485 q^{18} + 770 q^{19} - 7755 q^{20} - 12518 q^{21} - 10670 q^{22} - 10153 q^{23} - 20086 q^{24} - 693 q^{25} + 6941 q^{26} + 22132 q^{27} + 41525 q^{28} + 11220 q^{29} + 33605 q^{30} + 110 q^{31} - 31339 q^{32} - 41272 q^{33} - 76021 q^{34} - 15961 q^{35} + 48994 q^{36} + 72105 q^{37} + 95744 q^{38} + 61369 q^{39} + 68189 q^{40} + 671 q^{41} - 78221 q^{42} - 59367 q^{43} - 139348 q^{44} - 133672 q^{45} - 174163 q^{46} - 73106 q^{47} - 96195 q^{48} - 20141 q^{49} + 48114 q^{50} + 70873 q^{51} + 279279 q^{52} + 71951 q^{53} + 109989 q^{54} + 71467 q^{55} + 161414 q^{56} + 120538 q^{57} + 39028 q^{58} + 30459 q^{59} + 118679 q^{60} + 125169 q^{61} + 102685 q^{62} + 7194 q^{63} - 112651 q^{64} - 196438 q^{65} - 317724 q^{66} - 94369 q^{67} - 610390 q^{68} - 250536 q^{69} - 358710 q^{70} - 176286 q^{71} - 264572 q^{72} - 10549 q^{73} - 165880 q^{74} - 365772 q^{75} + 134794 q^{76} + 383108 q^{77} + 1021955 q^{78} + 657613 q^{79} + 1608530 q^{80} + 1283117 q^{81} + 573639 q^{82} + 168696 q^{83} - 88077 q^{84} - 302643 q^{85} - 805981 q^{86} - 481679 q^{87} - 490787 q^{88} - 453365 q^{89} - 1637042 q^{90} - 728750 q^{91} - 810722 q^{92} - 996490 q^{93} - 631884 q^{94} - 816530 q^{95} - 1481964 q^{96} - 306548 q^{97} + 216733 q^{98} + 1026586 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
23.6.a \(\chi_{23}(1, \cdot)\) 23.6.a.a 3 1
23.6.a.b 6
23.6.c \(\chi_{23}(2, \cdot)\) 23.6.c.a 90 10