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Properties

Label 10.7
Level 10
Weight 7
Dimension 6
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 42
Trace bound 0

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(42\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(10))\).

Total New Old
Modular forms 22 6 16
Cusp forms 14 6 8
Eisenstein series 8 0 8

Trace form

\( 6 q + 8 q^{2} - 64 q^{3} + 180 q^{5} + 224 q^{6} - 696 q^{7} - 256 q^{8} + O(q^{10}) \) \( 6 q + 8 q^{2} - 64 q^{3} + 180 q^{5} + 224 q^{6} - 696 q^{7} - 256 q^{8} + 2280 q^{10} + 472 q^{11} - 2048 q^{12} - 4614 q^{13} + 3320 q^{15} - 6144 q^{16} + 17554 q^{17} + 12152 q^{18} - 9920 q^{20} - 46408 q^{21} - 20544 q^{22} + 39616 q^{23} - 10350 q^{25} + 49584 q^{26} + 43160 q^{27} + 22272 q^{28} - 65280 q^{30} - 94608 q^{31} - 8192 q^{32} - 137848 q^{33} + 217240 q^{35} + 139328 q^{36} + 6414 q^{37} + 57760 q^{38} - 49920 q^{40} + 39352 q^{41} - 367424 q^{42} - 215184 q^{43} - 6710 q^{45} + 248544 q^{46} + 385824 q^{47} + 65536 q^{48} - 86600 q^{50} - 53168 q^{51} - 147648 q^{52} - 49954 q^{53} - 318840 q^{55} - 74752 q^{56} + 189680 q^{57} + 473280 q^{58} - 186880 q^{60} - 76728 q^{61} + 226976 q^{62} + 289376 q^{63} - 35130 q^{65} - 70912 q^{66} - 651936 q^{67} - 561728 q^{68} + 500640 q^{70} - 1126768 q^{71} + 388864 q^{72} + 664326 q^{73} + 1258600 q^{75} + 241920 q^{76} + 347528 q^{77} - 971616 q^{78} - 184320 q^{80} + 1686226 q^{81} + 724416 q^{82} - 1466904 q^{83} - 820710 q^{85} - 2975136 q^{86} - 2642560 q^{87} + 657408 q^{88} + 1096040 q^{90} + 2448672 q^{91} + 1267712 q^{92} + 4076792 q^{93} - 699400 q^{95} - 229376 q^{96} - 871866 q^{97} - 1286072 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.7.c \(\chi_{10}(3, \cdot)\) 10.7.c.a 2 2
10.7.c.b 4

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)