Properties

Label 23.11
Level 23
Weight 11
Dimension 209
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 484
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(484\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(23))\).

Total New Old
Modular forms 231 231 0
Cusp forms 209 209 0
Eisenstein series 22 22 0

Trace form

\( 209 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} + O(q^{10}) \) \( 209 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} - 11 q^{10} - 11 q^{11} - 11 q^{12} - 11 q^{13} - 11 q^{14} - 4830144 q^{15} + 7062517 q^{16} + 1092014 q^{17} - 21793035 q^{18} - 2415644 q^{19} + 25028597 q^{20} + 26277196 q^{21} - 25669413 q^{23} - 96949270 q^{24} - 4257737 q^{25} + 43269237 q^{26} + 99089914 q^{27} + 43862005 q^{28} - 39229894 q^{29} - 270003723 q^{30} - 1294832 q^{31} + 275686389 q^{32} - 54918402 q^{33} - 124580401 q^{34} - 219312511 q^{35} + 678768244 q^{36} + 518658261 q^{37} - 208458646 q^{38} - 692734691 q^{39} - 1236125011 q^{40} - 14679379 q^{41} + 1644990919 q^{42} + 997299501 q^{43} + 1314948338 q^{44} - 1802647363 q^{46} - 1479366350 q^{47} - 2714261011 q^{48} - 671617331 q^{49} + 1654296864 q^{50} + 2177981773 q^{51} + 6218950419 q^{52} + 679896965 q^{53} - 1880257731 q^{54} - 6583492465 q^{55} - 4503370696 q^{56} + 2289855898 q^{57} + 10407468654 q^{58} + 4315302629 q^{59} - 14840793781 q^{60} - 5311011871 q^{61} - 5764942667 q^{62} - 453734886 q^{63} + 7035944949 q^{64} + 10772645950 q^{65} + 12902167608 q^{66} + 2086349727 q^{67} - 5877567036 q^{69} - 16582863638 q^{70} - 11682273086 q^{71} - 21387471182 q^{72} - 956060061 q^{73} + 28336591052 q^{74} - 2688684416 q^{75} + 3533940894 q^{76} + 19704939188 q^{77} + 55417966659 q^{78} + 11295172361 q^{79} - 32343151082 q^{80} - 47619104071 q^{81} - 43271328529 q^{82} - 14758669948 q^{83} + 3906513611 q^{84} + 10651410495 q^{85} - 6838112941 q^{86} + 59998492741 q^{87} + 50131567101 q^{88} + 34310737417 q^{89} + 65550641882 q^{90} - 33937173182 q^{92} - 82509543358 q^{93} - 75841262728 q^{94} - 32523757684 q^{95} - 169612944512 q^{96} - 50355692024 q^{97} + 40099717229 q^{98} + 177617674300 q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(23))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
23.11.b \(\chi_{23}(22, \cdot)\) 23.11.b.a 3 1
23.11.b.b 16
23.11.d \(\chi_{23}(5, \cdot)\) 23.11.d.a 190 10