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Properties

Label 8.15
Level 8
Weight 15
Dimension 13
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 60
Trace bound 0

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 15 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(\Gamma_1(8))\).

Total New Old
Modular forms 31 15 16
Cusp forms 25 13 12
Eisenstein series 6 2 4

Trace form

\( 13 q + 90 q^{2} - 2 q^{3} - 14444 q^{4} + 131740 q^{6} - 3194760 q^{8} + 17537551 q^{9} + O(q^{10}) \) \( 13 q + 90 q^{2} - 2 q^{3} - 14444 q^{4} + 131740 q^{6} - 3194760 q^{8} + 17537551 q^{9} - 14533440 q^{10} + 10455534 q^{11} + 84432472 q^{12} + 191568384 q^{14} + 82613008 q^{16} - 58296678 q^{17} + 864073438 q^{18} - 702532066 q^{19} - 1679371200 q^{20} - 1912785028 q^{22} + 1243741840 q^{24} - 9753761195 q^{25} - 2773507776 q^{26} - 17884765988 q^{27} + 25329333120 q^{28} + 42207767040 q^{30} + 3949513440 q^{32} - 19239166252 q^{33} + 42415873460 q^{34} + 149949623040 q^{35} - 79327949732 q^{36} - 124918730532 q^{38} - 66999085440 q^{40} - 69106160886 q^{41} - 110343609600 q^{42} - 462759434770 q^{43} + 48714213144 q^{44} + 864780977664 q^{46} - 1576451470112 q^{48} + 31633842205 q^{49} - 1170035556630 q^{50} + 3762729232892 q^{51} + 798005307840 q^{52} + 1472720706808 q^{54} - 1050155264256 q^{56} - 2103342900748 q^{57} + 389204742720 q^{58} - 2691410604978 q^{59} + 4350689397120 q^{60} + 9957296947200 q^{62} - 12411624588224 q^{64} - 8069319822720 q^{65} - 21041652169048 q^{66} - 6598274286658 q^{67} + 26917470499368 q^{68} + 35197935521280 q^{70} - 52816980304088 q^{72} + 5198736923498 q^{73} - 55499920147776 q^{74} + 27523903144750 q^{75} + 62679317339864 q^{76} + 92515055193600 q^{78} - 86826189154560 q^{80} + 31705000182673 q^{81} - 103559585516908 q^{82} - 49920611458722 q^{83} + 186893160787200 q^{84} + 159615001426812 q^{86} - 248074163925232 q^{88} + 16347745386954 q^{89} - 488020221650880 q^{90} + 36699395136768 q^{91} + 413167093560960 q^{92} + 496016398930944 q^{94} - 719949436928960 q^{96} + 11024204172410 q^{97} - 610467423890310 q^{98} - 55227322255558 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(\Gamma_1(8))\)

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
8.15.c \(\chi_{8}(7, \cdot)\) None 0 1
8.15.d \(\chi_{8}(3, \cdot)\) 8.15.d.a 1 1
8.15.d.b 12

Decomposition of \(S_{15}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{15}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{15}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)