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Properties

Label 23.17
Level 23
Weight 17
Dimension 341
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 748
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 17 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(748\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(\Gamma_1(23))\).

Total New Old
Modular forms 363 363 0
Cusp forms 341 341 0
Eisenstein series 22 22 0

Trace form

\( 341 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} + O(q^{10}) \) \( 341 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} + 12152089092 q^{15} - 30102454283 q^{16} + 19673081494 q^{17} - 129589166091 q^{18} + 28069995712 q^{19} + 116253130741 q^{20} - 269655282644 q^{21} + 359388383299 q^{23} - 222646566934 q^{24} - 694510483865 q^{25} + 161586044917 q^{26} + 2014069092574 q^{27} - 832007700491 q^{28} - 1274406930038 q^{29} + 3925191852021 q^{30} + 1731439656628 q^{31} - 9122250424331 q^{32} + 9325683117894 q^{33} - 15462442158097 q^{34} + 6125212499989 q^{35} - 32954202027956 q^{36} + 29813993918709 q^{37} + 11019619240234 q^{38} - 42420672689483 q^{39} - 21553503125011 q^{40} + 26923013527861 q^{41} + 94769887187239 q^{42} - 50638409339595 q^{43} - 152847518739366 q^{44} + 241220907615677 q^{46} + 110748208697258 q^{47} - 125768401838035 q^{48} - 326015970422219 q^{49} - 218536376953136 q^{50} + 188897493178933 q^{51} + 902683726787139 q^{52} + 26427491680117 q^{53} - 1677721460284419 q^{54} + 59540702316623 q^{55} - 418074633891200 q^{56} + 571163301385138 q^{57} - 203071206956706 q^{58} + 82561631311225 q^{59} - 387105290039941 q^{60} - 1103480255827807 q^{61} + 57665564909557 q^{62} + 1658409032483214 q^{63} + 2507462036946933 q^{64} - 454628245219082 q^{65} - 3613994886545472 q^{66} - 906858396753705 q^{67} + 2799083538543204 q^{69} + 5744956374941674 q^{70} + 1175742059843494 q^{71} - 7137791590350806 q^{72} - 2169968228009901 q^{73} - 756860536492940 q^{74} + 3617043332639572 q^{75} + 22813539832516422 q^{76} - 1717897867564868 q^{77} - 18121559315484141 q^{78} - 2440785349512631 q^{79} + 1713956746742878 q^{80} + 4430081780154833 q^{81} + 327850494621023 q^{82} - 6777653695707752 q^{83} - 34301794735209925 q^{84} + 27218603894130363 q^{85} + 54853107166614691 q^{86} + 14779009686655093 q^{87} - 18504607147744707 q^{88} - 27468388628337899 q^{89} - 70947771022416046 q^{90} + 39301106723953162 q^{92} + 76688536304732330 q^{93} + 38438159156810336 q^{94} - 25117179793935944 q^{95} - 114954333609935336 q^{96} - 11204534181627644 q^{97} - 77841360115514963 q^{98} - 24858259519348112 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{17}^{\mathrm{new}}(\Gamma_1(23))\)

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
23.17.b \(\chi_{23}(22, \cdot)\) 23.17.b.a 3 1
23.17.b.b 28
23.17.d \(\chi_{23}(5, \cdot)\) 23.17.d.a 310 10