Properties

Label 30.6
Level 30
Weight 6
Dimension 28
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 288
Trace bound 1

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Defining parameters

Level: \( N \) = \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(288\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(30))\).

Total New Old
Modular forms 136 28 108
Cusp forms 104 28 76
Eisenstein series 32 0 32

Trace form

\( 28q + 14q^{3} - 64q^{4} - 104q^{5} + 152q^{6} + 272q^{7} - 324q^{9} + O(q^{10}) \) \( 28q + 14q^{3} - 64q^{4} - 104q^{5} + 152q^{6} + 272q^{7} - 324q^{9} - 368q^{10} + 80q^{11} + 352q^{12} + 3184q^{13} - 1408q^{14} + 2930q^{15} - 3072q^{16} - 3144q^{17} - 2272q^{18} + 2224q^{19} + 1664q^{20} + 3128q^{21} - 3296q^{22} - 6024q^{23} - 1152q^{24} - 18660q^{25} - 576q^{26} + 18014q^{27} + 4352q^{28} + 2976q^{29} + 9384q^{30} + 42144q^{31} - 1096q^{33} - 19008q^{34} - 40576q^{35} - 2752q^{36} - 55616q^{37} - 5664q^{38} - 11844q^{39} + 3840q^{40} + 24992q^{41} + 42112q^{42} + 57184q^{43} + 22144q^{44} + 40336q^{45} + 51200q^{46} + 12432q^{47} + 5632q^{48} - 42780q^{49} - 21152q^{50} - 183572q^{51} - 33536q^{52} - 1968q^{53} - 5832q^{54} - 106896q^{55} + 5632q^{56} + 161408q^{57} + 3584q^{58} + 97640q^{59} + 22304q^{60} + 250120q^{61} + 17376q^{62} - 203488q^{63} - 16384q^{64} - 140112q^{65} - 135520q^{66} - 151120q^{67} - 50304q^{68} - 206352q^{69} - 88704q^{70} + 6720q^{71} + 36352q^{72} + 477384q^{73} + 309728q^{74} + 463990q^{75} + 19968q^{76} + 118464q^{77} - 56112q^{78} - 232568q^{79} - 26624q^{80} - 229772q^{81} - 285824q^{82} + 46464q^{83} - 5760q^{84} - 111128q^{85} - 128288q^{86} + 184796q^{87} - 52736q^{88} + 10792q^{89} - 106960q^{90} + 309536q^{91} - 96384q^{92} - 249712q^{93} + 174336q^{94} - 33000q^{95} - 2048q^{96} - 327968q^{97} - 103488q^{98} + 112104q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
30.6.a \(\chi_{30}(1, \cdot)\) 30.6.a.a 1 1
30.6.a.b 1
30.6.c \(\chi_{30}(19, \cdot)\) 30.6.c.a 2 1
30.6.c.b 4
30.6.e \(\chi_{30}(17, \cdot)\) 30.6.e.a 20 2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(30))\) into lower level spaces

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