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Properties

Label 8.8
Level 8
Weight 8
Dimension 8
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 32
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(32\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 17 10 7
Cusp forms 11 8 3
Eisenstein series 6 2 4

Trace form

\( 8 q + 6 q^{2} - 40 q^{3} + 116 q^{4} + 348 q^{5} + 268 q^{6} - 2368 q^{7} + 1512 q^{8} + 1700 q^{9} + O(q^{10}) \) \( 8 q + 6 q^{2} - 40 q^{3} + 116 q^{4} + 348 q^{5} + 268 q^{6} - 2368 q^{7} + 1512 q^{8} + 1700 q^{9} - 1656 q^{10} - 5688 q^{11} - 4088 q^{12} - 4660 q^{13} + 12048 q^{14} + 43680 q^{15} + 35344 q^{16} - 25968 q^{17} - 89062 q^{18} - 1352 q^{19} - 114768 q^{20} - 15552 q^{21} + 152860 q^{22} + 81984 q^{23} + 282512 q^{24} - 3940 q^{25} - 316968 q^{26} - 332560 q^{27} - 480800 q^{28} + 222636 q^{29} + 821648 q^{30} + 121600 q^{31} + 817056 q^{32} + 126680 q^{33} - 1009108 q^{34} - 488928 q^{35} - 1253556 q^{36} - 471780 q^{37} + 974124 q^{38} + 846336 q^{39} + 954464 q^{40} + 343248 q^{41} - 1093088 q^{42} + 20360 q^{43} - 1096344 q^{44} - 507188 q^{45} + 929840 q^{46} + 1168512 q^{47} + 853920 q^{48} - 452024 q^{49} - 148626 q^{50} + 220720 q^{51} + 823952 q^{52} + 2109180 q^{53} - 1077064 q^{54} - 4423808 q^{55} - 2468928 q^{56} - 2477256 q^{57} + 3130744 q^{58} - 1863576 q^{59} + 5715168 q^{60} + 1002860 q^{61} - 7055808 q^{62} + 3863776 q^{63} - 4792768 q^{64} + 4931016 q^{65} + 7926264 q^{66} + 7625560 q^{67} + 6608040 q^{68} - 6793792 q^{69} - 7406912 q^{70} - 12856128 q^{71} - 11363944 q^{72} - 5261616 q^{73} + 7744200 q^{74} + 10695784 q^{75} + 9241288 q^{76} + 5023680 q^{77} - 9471184 q^{78} + 14929792 q^{79} - 12600384 q^{80} + 3381600 q^{81} + 10715932 q^{82} - 6949320 q^{83} + 4220608 q^{84} - 6081800 q^{85} - 5639076 q^{86} - 40431936 q^{87} + 1541200 q^{88} + 7301712 q^{89} - 121864 q^{90} - 2573664 q^{91} + 669600 q^{92} + 14460160 q^{93} + 15503712 q^{94} + 45845088 q^{95} + 21402176 q^{96} + 3777552 q^{97} - 14983242 q^{98} - 11495192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
8.8.a \(\chi_{8}(1, \cdot)\) 8.8.a.a 1 1
8.8.a.b 1
8.8.b \(\chi_{8}(5, \cdot)\) 8.8.b.a 6 1

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

\( S_{8}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)