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Properties

Label 30.7
Level 30
Weight 7
Dimension 32
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 336
Trace bound 2

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Defining parameters

Level: \( N \) = \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(336\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(30))\).

Total New Old
Modular forms 160 32 128
Cusp forms 128 32 96
Eisenstein series 32 0 32

Trace form

\( 32 q - 16 q^{2} - 20 q^{3} + 128 q^{4} - 360 q^{5} + 160 q^{6} + 1384 q^{7} + 512 q^{8} + 668 q^{9} + O(q^{10}) \) \( 32 q - 16 q^{2} - 20 q^{3} + 128 q^{4} - 360 q^{5} + 160 q^{6} + 1384 q^{7} + 512 q^{8} + 668 q^{9} - 3792 q^{10} - 3248 q^{11} + 640 q^{12} + 13732 q^{13} + 5704 q^{15} + 8192 q^{16} - 10916 q^{17} + 14672 q^{18} - 36392 q^{19} + 1408 q^{20} - 416 q^{21} + 34944 q^{22} + 12064 q^{23} - 12288 q^{24} - 18184 q^{25} - 99168 q^{26} - 45980 q^{27} - 44288 q^{28} + 24960 q^{30} + 174520 q^{31} + 16384 q^{32} + 100632 q^{33} + 122496 q^{34} - 205952 q^{35} + 99072 q^{36} - 61508 q^{37} - 137984 q^{38} - 175720 q^{39} + 1536 q^{40} - 221264 q^{41} + 71488 q^{42} + 111928 q^{43} + 226620 q^{45} - 188736 q^{46} - 197664 q^{47} - 20480 q^{48} + 1599300 q^{49} + 479632 q^{50} + 551984 q^{51} - 223616 q^{52} - 786700 q^{53} - 287040 q^{54} - 1256016 q^{55} - 53248 q^{56} - 984472 q^{57} - 216576 q^{58} + 127488 q^{60} + 1032712 q^{61} + 537920 q^{62} + 1717952 q^{63} + 131072 q^{64} + 1169556 q^{65} - 48128 q^{66} - 1011176 q^{67} + 349312 q^{68} - 3203408 q^{69} - 2346048 q^{70} - 1749088 q^{71} - 718336 q^{72} - 959108 q^{73} + 1596596 q^{75} + 1221376 q^{76} + 4441712 q^{77} + 2001376 q^{78} + 2080552 q^{79} + 368640 q^{80} - 224328 q^{81} - 989568 q^{82} + 700512 q^{83} - 578304 q^{84} - 5798964 q^{85} - 120192 q^{86} - 5144688 q^{87} - 1118208 q^{88} + 2369136 q^{90} + 3219824 q^{91} + 386048 q^{92} + 3953504 q^{93} + 4419840 q^{94} + 3279584 q^{95} + 163840 q^{96} + 2800492 q^{97} - 2034704 q^{98} - 6616528 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(30))\)

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
30.7.b \(\chi_{30}(29, \cdot)\) 30.7.b.a 12 1
30.7.d \(\chi_{30}(11, \cdot)\) 30.7.d.a 8 1
30.7.f \(\chi_{30}(7, \cdot)\) 30.7.f.a 4 2
30.7.f.b 8

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(30))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(30)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)