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Properties

Label 7.8
Level 7
Weight 8
Dimension 11
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 32
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
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 \(M_{8}(\Gamma_1(7))\).

Total New Old
Modular forms 17 15 2
Cusp forms 11 11 0
Eisenstein series 6 4 2

Trace form

\( 11 q - 3 q^{2} + 24 q^{3} - 259 q^{4} - 6 q^{5} + 1290 q^{6} + 329 q^{7} - 1833 q^{8} - 657 q^{9} + O(q^{10}) \) \( 11 q - 3 q^{2} + 24 q^{3} - 259 q^{4} - 6 q^{5} + 1290 q^{6} + 329 q^{7} - 1833 q^{8} - 657 q^{9} - 9090 q^{10} + 1248 q^{11} + 20370 q^{12} - 4970 q^{13} + 46473 q^{14} - 5424 q^{15} - 89071 q^{16} - 71838 q^{17} - 45525 q^{18} + 46432 q^{19} + 375312 q^{20} + 141876 q^{21} - 226596 q^{22} - 229596 q^{23} - 472182 q^{24} - 61603 q^{25} + 294924 q^{26} + 528096 q^{27} + 587909 q^{28} + 130362 q^{29} - 1008786 q^{30} - 642716 q^{31} + 397719 q^{32} + 243132 q^{33} + 110238 q^{34} - 101598 q^{35} - 276783 q^{36} + 236422 q^{37} - 42144 q^{38} - 792288 q^{39} + 280008 q^{40} + 1045254 q^{41} + 190638 q^{42} - 559460 q^{43} + 2084964 q^{44} + 2350998 q^{45} - 842466 q^{46} - 3078228 q^{47} - 5738178 q^{48} - 2440837 q^{49} + 1878045 q^{50} + 2522532 q^{51} + 4828684 q^{52} + 3442014 q^{53} + 1151898 q^{54} - 5691408 q^{55} - 5335953 q^{56} + 5192496 q^{57} + 5748450 q^{58} + 1387200 q^{59} + 776580 q^{60} - 5179166 q^{61} - 7431576 q^{62} - 7166187 q^{63} - 2494543 q^{64} + 1905036 q^{65} + 5688126 q^{66} + 2371672 q^{67} - 881118 q^{68} + 13396392 q^{69} + 13492122 q^{70} + 759816 q^{71} - 3483969 q^{72} - 4226366 q^{73} - 15105120 q^{74} - 4136340 q^{75} + 2608018 q^{76} - 8195880 q^{77} - 16075920 q^{78} - 12023924 q^{79} - 16216512 q^{80} + 11466495 q^{81} + 29779974 q^{82} + 31439940 q^{83} + 35605458 q^{84} + 16342740 q^{85} - 19050576 q^{86} - 26728080 q^{87} - 2647104 q^{88} - 834462 q^{89} - 12292836 q^{90} - 5051018 q^{91} - 31021080 q^{92} - 35113668 q^{93} - 16931814 q^{94} + 320172 q^{95} + 34491954 q^{96} + 23705710 q^{97} + 59196165 q^{98} + 25873884 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)

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
7.8.a \(\chi_{7}(1, \cdot)\) 7.8.a.a 1 1
7.8.a.b 2
7.8.c \(\chi_{7}(2, \cdot)\) 7.8.c.a 8 2