Properties

Label 7.6
Level 7
Weight 6
Dimension 7
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 24
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(24\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(7))\).

Total New Old
Modular forms 13 11 2
Cusp forms 7 7 0
Eisenstein series 6 4 2

Trace form

\( 7 q - 3 q^{2} - 12 q^{3} + 61 q^{4} - 36 q^{5} - 222 q^{6} - 119 q^{7} - 177 q^{8} + 891 q^{9} + O(q^{10}) \) \( 7 q - 3 q^{2} - 12 q^{3} + 61 q^{4} - 36 q^{5} - 222 q^{6} - 119 q^{7} - 177 q^{8} + 891 q^{9} + 1542 q^{10} + 204 q^{11} - 2310 q^{12} - 2338 q^{13} - 1743 q^{14} + 912 q^{15} + 3601 q^{16} + 2424 q^{17} + 3795 q^{18} - 3004 q^{19} - 4704 q^{20} - 1134 q^{21} + 180 q^{22} + 3924 q^{23} + 1794 q^{24} - 5099 q^{25} + 2268 q^{26} + 3432 q^{27} - 539 q^{28} - 3990 q^{29} - 19866 q^{30} - 11212 q^{31} - 753 q^{32} + 20166 q^{33} + 37998 q^{34} + 29358 q^{35} + 5241 q^{36} - 15256 q^{37} - 34368 q^{38} - 20160 q^{39} + 7440 q^{40} - 17010 q^{41} - 20034 q^{42} - 17500 q^{43} - 20988 q^{44} + 6570 q^{45} + 12462 q^{46} + 43980 q^{47} + 43710 q^{48} + 12103 q^{49} + 40173 q^{50} + 32088 q^{51} + 23324 q^{52} + 8688 q^{53} - 111054 q^{54} - 102048 q^{55} - 40593 q^{56} - 23868 q^{57} + 61986 q^{58} + 19140 q^{59} + 41244 q^{60} + 3380 q^{61} - 6984 q^{62} + 24885 q^{63} - 18239 q^{64} + 50064 q^{65} + 125190 q^{66} - 65932 q^{67} - 137550 q^{68} - 118620 q^{69} - 130494 q^{70} + 34440 q^{71} + 58143 q^{72} + 136040 q^{73} + 194784 q^{74} + 75948 q^{75} + 58226 q^{76} + 73374 q^{77} - 37632 q^{78} + 74036 q^{79} - 218832 q^{80} - 157671 q^{81} + 53550 q^{82} - 111636 q^{83} + 14994 q^{84} - 47640 q^{85} - 345624 q^{86} - 191040 q^{87} - 103680 q^{88} + 60360 q^{89} + 328836 q^{90} + 125342 q^{91} + 254376 q^{92} - 23982 q^{93} - 31806 q^{94} + 227892 q^{95} + 239106 q^{96} + 380534 q^{97} + 96285 q^{98} - 161532 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
7.6.a \(\chi_{7}(1, \cdot)\) 7.6.a.a 1 1
7.6.a.b 2
7.6.c \(\chi_{7}(2, \cdot)\) 7.6.c.a 4 2