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Properties

Label 23.8
Level 23
Weight 8
Dimension 143
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 352
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(352\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(23))\).

Total New Old
Modular forms 165 163 2
Cusp forms 143 143 0
Eisenstein series 22 20 2

Trace form

\( 143 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} + O(q^{10}) \) \( 143 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} - 11 q^{10} - 11 q^{11} - 11 q^{12} - 11 q^{13} - 11 q^{14} - 3850 q^{15} + 128117 q^{16} - 10318 q^{17} - 278443 q^{18} - 62370 q^{19} - 2827 q^{20} + 221716 q^{21} + 234234 q^{22} + 200343 q^{23} + 122474 q^{24} - 192049 q^{25} - 399003 q^{26} - 690272 q^{27} - 554763 q^{28} + 83930 q^{29} + 1480853 q^{30} + 530838 q^{31} + 404085 q^{32} - 1215214 q^{33} - 1815957 q^{34} + 1273239 q^{35} + 3648634 q^{36} + 905201 q^{37} - 1711776 q^{38} - 2778743 q^{39} - 5863011 q^{40} - 969573 q^{41} - 537581 q^{42} + 1694297 q^{43} + 5680180 q^{44} + 6014228 q^{45} + 7468461 q^{46} + 2398110 q^{47} + 428637 q^{48} - 3578729 q^{49} - 8421886 q^{50} - 6395015 q^{51} - 16253281 q^{52} - 2342637 q^{53} - 11169411 q^{54} + 7243291 q^{55} + 31363662 q^{56} + 20789560 q^{57} + 16569652 q^{58} - 5494709 q^{59} - 40608601 q^{60} - 11102839 q^{61} - 15633563 q^{62} - 9022926 q^{63} - 4685835 q^{64} + 5549456 q^{65} + 16534716 q^{66} + 6031575 q^{67} + 41505002 q^{68} + 16515774 q^{69} + 20322346 q^{70} + 6254754 q^{71} - 4822532 q^{72} - 4352337 q^{73} - 55910624 q^{74} - 53035488 q^{75} - 15797342 q^{76} + 9091786 q^{77} + 49703291 q^{78} + 12287341 q^{79} + 27083210 q^{80} - 19645747 q^{81} + 1235399 q^{82} + 1403468 q^{83} - 57841245 q^{84} - 60870139 q^{85} - 81738965 q^{86} + 5166865 q^{87} + 26061981 q^{88} + 34446775 q^{89} + 142296022 q^{90} + 66314226 q^{91} + 72107926 q^{92} + 79748702 q^{93} + 38685900 q^{94} - 32629850 q^{95} - 73573764 q^{96} - 3562394 q^{97} - 5377427 q^{98} - 58260554 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(23))\)

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
23.8.a \(\chi_{23}(1, \cdot)\) 23.8.a.a 5 1
23.8.a.b 8
23.8.c \(\chi_{23}(2, \cdot)\) 23.8.c.a 130 10