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Properties

Label 23.3
Level 23
Weight 3
Dimension 33
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 132
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(132\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(23))\).

Total New Old
Modular forms 55 55 0
Cusp forms 33 33 0
Eisenstein series 22 22 0

Trace form

\( 33 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} + O(q^{10}) \) \( 33 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} - 11 q^{10} - 11 q^{11} - 11 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 121 q^{16} + 44 q^{17} + 165 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} - 33 q^{23} - 154 q^{24} - 77 q^{25} - 99 q^{26} - 176 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 231 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 484 q^{36} + 341 q^{37} + 374 q^{38} + 253 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 319 q^{48} - 275 q^{49} - 396 q^{50} - 275 q^{51} - 781 q^{52} - 187 q^{53} - 495 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 286 q^{58} + 77 q^{59} + 539 q^{60} + 297 q^{61} + 385 q^{62} + 264 q^{63} + 341 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 638 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 759 q^{78} + 33 q^{79} - 242 q^{80} + 737 q^{81} - 33 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 517 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} - 110 q^{92} - 286 q^{93} - 352 q^{94} - 154 q^{95} - 440 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(23))\)

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
23.3.b \(\chi_{23}(22, \cdot)\) 23.3.b.a 3 1
23.3.d \(\chi_{23}(5, \cdot)\) 23.3.d.a 30 10