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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

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

Display 100 coefficients 10 coefficients

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 available 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

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