Properties

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

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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

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

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

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