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Properties

Label 23.5
Level 23
Weight 5
Dimension 77
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 220
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(220\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(23))\).

Total New Old
Modular forms 99 99 0
Cusp forms 77 77 0
Eisenstein series 22 22 0

Trace form

\( 77 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} + O(q^{10}) \) \( 77 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} - 11 q^{10} - 11 q^{11} - 11 q^{12} - 11 q^{13} - 11 q^{14} + 1452 q^{15} + 517 q^{16} - 506 q^{17} - 3531 q^{18} - 968 q^{19} - 3179 q^{20} - 1364 q^{21} + 979 q^{23} + 5786 q^{24} + 2695 q^{25} + 3157 q^{26} + 4774 q^{27} + 5269 q^{28} + 682 q^{29} - 1419 q^{30} - 1892 q^{31} - 7931 q^{32} - 6666 q^{33} + 12815 q^{34} + 6589 q^{35} + 4444 q^{36} - 3531 q^{37} - 10406 q^{38} - 11099 q^{39} - 24211 q^{40} - 5819 q^{41} - 24761 q^{42} - 7227 q^{43} - 6534 q^{44} + 7997 q^{46} + 7898 q^{47} + 22781 q^{48} + 21637 q^{49} + 28864 q^{50} + 17413 q^{51} + 42339 q^{52} + 7381 q^{53} + 48477 q^{54} + 21263 q^{55} + 19888 q^{56} - 13310 q^{57} - 44946 q^{58} - 38687 q^{59} - 83941 q^{60} - 22495 q^{61} - 34859 q^{62} - 27786 q^{63} - 39435 q^{64} - 27962 q^{65} - 21648 q^{66} - 2937 q^{67} + 7524 q^{69} + 23914 q^{70} + 21934 q^{71} + 66682 q^{72} + 13299 q^{73} + 85492 q^{74} + 129052 q^{75} + 122166 q^{76} + 61996 q^{77} + 55539 q^{78} + 10505 q^{79} - 21362 q^{80} - 85855 q^{81} - 69025 q^{82} - 65120 q^{83} - 221221 q^{84} - 132957 q^{85} - 141053 q^{86} - 83435 q^{87} - 41283 q^{88} - 22979 q^{89} - 37246 q^{90} + 18106 q^{92} + 48026 q^{93} + 52976 q^{94} + 96976 q^{95} + 276232 q^{96} + 115852 q^{97} + 132781 q^{98} + 163768 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(23))\)

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
23.5.b \(\chi_{23}(22, \cdot)\) 23.5.b.a 3 1
23.5.b.b 4
23.5.d \(\chi_{23}(5, \cdot)\) 23.5.d.a 70 10