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Properties

Label 30.4
Level 30
Weight 4
Dimension 16
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 192
Trace bound 3

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Defining parameters

Level: \( N \) = \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(192\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(30))\).

Total New Old
Modular forms 88 16 72
Cusp forms 56 16 40
Eisenstein series 32 0 32

Trace form

\( 16 q + 14 q^{3} + 4 q^{5} - 4 q^{6} + 40 q^{7} + O(q^{10}) \) \( 16 q + 14 q^{3} + 4 q^{5} - 4 q^{6} + 40 q^{7} - 40 q^{10} + 32 q^{11} - 8 q^{12} - 152 q^{13} - 64 q^{14} - 238 q^{15} - 128 q^{16} - 72 q^{17} - 16 q^{18} + 16 q^{19} - 16 q^{20} + 560 q^{21} + 336 q^{22} + 72 q^{23} + 48 q^{24} + 320 q^{25} + 288 q^{26} - 634 q^{27} + 160 q^{28} - 216 q^{29} + 84 q^{30} - 48 q^{31} + 464 q^{33} - 224 q^{34} + 224 q^{35} + 512 q^{36} + 568 q^{37} + 432 q^{38} + 228 q^{39} - 96 q^{40} - 376 q^{41} - 1088 q^{42} - 2648 q^{43} - 992 q^{44} - 1364 q^{45} - 1408 q^{46} - 144 q^{47} - 32 q^{48} + 1032 q^{49} - 176 q^{50} + 172 q^{51} + 352 q^{52} + 144 q^{53} + 108 q^{54} + 1792 q^{55} - 320 q^{56} + 1160 q^{57} + 2688 q^{58} + 1640 q^{59} + 1160 q^{60} + 560 q^{61} + 1008 q^{62} + 1520 q^{63} + 1008 q^{65} + 176 q^{66} - 344 q^{67} - 288 q^{68} - 384 q^{69} - 2880 q^{70} - 1728 q^{71} + 64 q^{72} + 448 q^{73} + 80 q^{74} - 1226 q^{75} - 704 q^{76} - 1728 q^{77} - 3864 q^{78} - 2072 q^{79} + 64 q^{80} - 3992 q^{81} + 1344 q^{82} - 1152 q^{83} + 288 q^{84} - 608 q^{85} + 1456 q^{86} + 4268 q^{87} + 1344 q^{88} + 1408 q^{89} + 5384 q^{90} + 2768 q^{91} + 288 q^{92} + 704 q^{93} + 2432 q^{94} - 1176 q^{95} - 320 q^{96} - 8936 q^{97} - 2016 q^{98} - 2232 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)

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
30.4.a \(\chi_{30}(1, \cdot)\) 30.4.a.a 1 1
30.4.a.b 1
30.4.c \(\chi_{30}(19, \cdot)\) 30.4.c.a 2 1
30.4.e \(\chi_{30}(17, \cdot)\) 30.4.e.a 12 2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(30))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(30)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 1}\)