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Properties

Label 60.4
Level 60
Weight 4
Dimension 108
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 768
Trace bound 3

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Defining parameters

Level: \( N \) = \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(768\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(60))\).

Total New Old
Modular forms 328 116 212
Cusp forms 248 108 140
Eisenstein series 80 8 72

Trace form

\( 108 q - 10 q^{3} + 8 q^{4} - 20 q^{5} + 32 q^{6} + 16 q^{7} + 84 q^{8} + 16 q^{9} + O(q^{10}) \) \( 108 q - 10 q^{3} + 8 q^{4} - 20 q^{5} + 32 q^{6} + 16 q^{7} + 84 q^{8} + 16 q^{9} + 60 q^{10} - 16 q^{11} - 164 q^{12} - 76 q^{13} + 50 q^{15} + 64 q^{16} + 284 q^{17} + 256 q^{18} + 400 q^{19} - 380 q^{20} - 128 q^{21} - 776 q^{22} - 264 q^{23} - 552 q^{24} - 1068 q^{25} + 368 q^{26} - 346 q^{27} + 1368 q^{28} + 120 q^{29} + 316 q^{30} + 144 q^{31} + 340 q^{32} + 136 q^{33} - 936 q^{34} + 80 q^{35} - 208 q^{36} + 460 q^{37} - 2032 q^{38} + 60 q^{39} - 2704 q^{40} - 872 q^{41} - 888 q^{42} + 640 q^{43} + 1040 q^{45} + 3208 q^{46} + 336 q^{47} + 1740 q^{48} - 624 q^{49} + 3184 q^{50} + 1276 q^{51} + 3000 q^{52} + 44 q^{53} - 80 q^{54} - 1520 q^{55} - 1472 q^{56} - 352 q^{57} + 88 q^{58} - 760 q^{59} + 1216 q^{60} + 336 q^{61} - 1672 q^{62} - 3040 q^{63} - 952 q^{64} + 2620 q^{65} + 224 q^{66} + 1648 q^{67} + 4432 q^{68} + 712 q^{69} + 4552 q^{70} + 2400 q^{71} + 1068 q^{72} - 1212 q^{73} + 4270 q^{75} - 2432 q^{76} - 1680 q^{77} - 2864 q^{78} + 280 q^{79} - 4636 q^{80} + 2220 q^{81} - 2008 q^{82} - 1344 q^{83} - 4264 q^{84} - 10580 q^{85} - 448 q^{86} - 5236 q^{87} + 808 q^{88} - 320 q^{89} - 3780 q^{90} - 5248 q^{91} - 2888 q^{92} - 9632 q^{93} - 5048 q^{94} - 1800 q^{95} - 5248 q^{96} + 8492 q^{97} - 3288 q^{98} + 360 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)

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
60.4.a \(\chi_{60}(1, \cdot)\) 60.4.a.a 1 1
60.4.a.b 1
60.4.d \(\chi_{60}(49, \cdot)\) 60.4.d.a 2 1
60.4.e \(\chi_{60}(11, \cdot)\) 60.4.e.a 24 1
60.4.h \(\chi_{60}(59, \cdot)\) 60.4.h.a 4 1
60.4.h.b 4
60.4.h.c 24
60.4.i \(\chi_{60}(17, \cdot)\) 60.4.i.a 4 2
60.4.i.b 8
60.4.j \(\chi_{60}(7, \cdot)\) 60.4.j.a 8 2
60.4.j.b 28

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(60))\) into lower level spaces

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