Properties

Label 60.7
Level 60
Weight 7
Dimension 228
Nonzero newspaces 6
Newform subspaces 6
Sturm bound 1344
Trace bound 5

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 6 \)
Sturm bound: \(1344\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(60))\).

Total New Old
Modular forms 616 244 372
Cusp forms 536 228 308
Eisenstein series 80 16 64

Trace form

\( 228 q + 20 q^{2} - 20 q^{3} - 312 q^{4} + 356 q^{5} - 4 q^{6} - 440 q^{7} - 340 q^{8} + 5120 q^{9} + O(q^{10}) \) \( 228 q + 20 q^{2} - 20 q^{3} - 312 q^{4} + 356 q^{5} - 4 q^{6} - 440 q^{7} - 340 q^{8} + 5120 q^{9} - 4264 q^{10} - 3248 q^{11} - 1460 q^{12} - 3508 q^{13} + 12888 q^{14} + 9016 q^{15} + 4528 q^{16} - 5540 q^{17} - 17604 q^{18} - 15464 q^{19} + 4812 q^{20} - 7688 q^{21} + 71224 q^{22} - 23840 q^{23} + 15552 q^{24} + 92508 q^{25} + 43800 q^{26} - 18620 q^{27} + 2056 q^{28} + 95880 q^{29} + 58568 q^{30} - 51272 q^{31} - 10700 q^{32} - 149680 q^{33} - 329688 q^{34} + 102976 q^{35} - 25784 q^{36} + 199940 q^{37} + 215800 q^{38} - 5704 q^{39} + 93368 q^{40} - 49320 q^{41} - 170104 q^{42} - 223880 q^{43} - 320776 q^{44} - 22664 q^{45} + 465256 q^{46} + 381600 q^{47} + 170356 q^{48} - 200808 q^{49} - 128948 q^{50} + 243248 q^{51} + 9264 q^{52} - 1044620 q^{53} - 78732 q^{54} + 444912 q^{55} - 1843840 q^{56} + 56048 q^{57} - 1696280 q^{58} + 816352 q^{60} + 546240 q^{61} + 1948520 q^{62} + 406400 q^{63} + 935304 q^{64} - 233692 q^{65} - 829680 q^{66} + 1157080 q^{67} + 572680 q^{68} - 1229936 q^{69} - 1406936 q^{70} + 202400 q^{71} - 62940 q^{72} - 224716 q^{73} - 1201488 q^{74} - 456268 q^{75} - 1488976 q^{76} - 1064560 q^{77} - 80088 q^{78} + 1334248 q^{79} + 1414972 q^{80} + 2310204 q^{81} + 1019640 q^{82} + 1894560 q^{83} + 2115072 q^{84} - 319964 q^{85} + 6939120 q^{86} - 2536080 q^{87} - 127160 q^{88} - 3372328 q^{89} + 285072 q^{90} + 2286320 q^{91} - 3040560 q^{92} - 1004672 q^{93} - 6910344 q^{94} - 2620000 q^{95} - 4732240 q^{96} - 4019548 q^{97} - 2709660 q^{98} + 4282160 q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(60))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
60.7.b \(\chi_{60}(29, \cdot)\) 60.7.b.a 12 1
60.7.c \(\chi_{60}(31, \cdot)\) 60.7.c.a 24 1
60.7.f \(\chi_{60}(19, \cdot)\) 60.7.f.a 36 1
60.7.g \(\chi_{60}(41, \cdot)\) 60.7.g.a 8 1
60.7.k \(\chi_{60}(13, \cdot)\) 60.7.k.a 12 2
60.7.l \(\chi_{60}(23, \cdot)\) 60.7.l.a 136 2

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(60))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(60)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)