Properties

Label 6.7
Level 6
Weight 7
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 14
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(14\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 8 2 6
Cusp forms 4 2 2
Eisenstein series 4 0 4

Trace form

\( 2 q + 42 q^{3} - 64 q^{4} - 192 q^{6} + 4 q^{7} + 306 q^{9} + O(q^{10}) \) \( 2 q + 42 q^{3} - 64 q^{4} - 192 q^{6} + 4 q^{7} + 306 q^{9} + 1920 q^{10} - 1344 q^{12} - 5900 q^{13} + 5760 q^{15} + 2048 q^{16} - 8064 q^{18} + 10516 q^{19} + 84 q^{21} + 384 q^{22} + 6144 q^{24} - 26350 q^{25} - 17766 q^{27} - 128 q^{28} + 40320 q^{30} + 45796 q^{31} + 1152 q^{33} - 50688 q^{34} - 9792 q^{36} + 68116 q^{37} - 123900 q^{39} - 61440 q^{40} - 384 q^{42} - 12812 q^{43} + 241920 q^{45} + 115968 q^{46} + 43008 q^{48} - 235290 q^{49} - 152064 q^{51} + 188800 q^{52} - 198720 q^{54} - 11520 q^{55} + 220836 q^{57} - 24960 q^{58} - 184320 q^{60} - 125132 q^{61} + 612 q^{63} - 65536 q^{64} + 8064 q^{66} + 877396 q^{67} + 347904 q^{69} + 3840 q^{70} + 258048 q^{72} - 1461020 q^{73} - 553350 q^{75} - 336512 q^{76} + 566400 q^{78} + 681124 q^{79} - 969246 q^{81} + 189696 q^{82} - 2688 q^{84} + 1520640 q^{85} - 74880 q^{87} - 12288 q^{88} + 293760 q^{90} - 11800 q^{91} + 961716 q^{93} - 2035200 q^{94} - 196608 q^{96} - 562172 q^{97} + 48384 q^{99} + O(q^{100}) \)

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

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
6.7.b \(\chi_{6}(5, \cdot)\) 6.7.b.a 2 1

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(6))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(6)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)