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Properties

Label 60.8
Level 60
Weight 8
Dimension 258
Nonzero newspaces 6
Newform subspaces 12
Sturm bound 1536
Trace bound 1

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Defining parameters

Level: \( N \) = \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 12 \)
Sturm bound: \(1536\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(60))\).

Total New Old
Modular forms 712 266 446
Cusp forms 632 258 374
Eisenstein series 80 8 72

Trace form

\( 258 q + 26 q^{3} - 56 q^{4} + 170 q^{5} + 320 q^{6} - 2468 q^{7} + 2004 q^{8} - 3698 q^{9} + O(q^{10}) \) \( 258 q + 26 q^{3} - 56 q^{4} + 170 q^{5} + 320 q^{6} - 2468 q^{7} + 2004 q^{8} - 3698 q^{9} + 8380 q^{10} + 10360 q^{11} - 12548 q^{12} - 22832 q^{13} + 3890 q^{15} + 118336 q^{16} + 36100 q^{17} - 32672 q^{18} + 12320 q^{19} - 113980 q^{20} - 33500 q^{21} + 29176 q^{22} + 6720 q^{23} + 170904 q^{24} - 1023438 q^{25} - 213008 q^{26} - 202 q^{27} + 67992 q^{28} + 307548 q^{29} - 275204 q^{30} + 294792 q^{31} + 35540 q^{32} + 38476 q^{33} - 6312 q^{34} - 819680 q^{35} - 1610896 q^{36} - 781000 q^{37} - 1098032 q^{38} + 1049760 q^{39} + 1068656 q^{40} - 666388 q^{41} + 3961896 q^{42} - 932476 q^{43} - 476770 q^{45} - 4076280 q^{46} + 408000 q^{47} - 3735540 q^{48} + 861174 q^{49} - 4816 q^{50} + 2219620 q^{51} + 12438200 q^{52} + 738412 q^{53} + 8756944 q^{54} - 4384680 q^{55} - 6547648 q^{56} - 2518300 q^{57} - 14951208 q^{58} + 6556888 q^{59} - 4238624 q^{60} + 1234492 q^{61} - 2193032 q^{62} - 13816 q^{63} + 22885192 q^{64} - 8808580 q^{65} + 17076512 q^{66} - 267668 q^{67} + 8043152 q^{68} + 24736 q^{69} + 7156552 q^{70} - 760800 q^{71} - 15593556 q^{72} + 15614424 q^{73} - 1583510 q^{75} + 12792064 q^{76} - 8807184 q^{77} + 30024208 q^{78} - 12149464 q^{79} - 20744156 q^{80} - 50734566 q^{81} - 8232408 q^{82} - 8690880 q^{83} - 45840424 q^{84} + 55312240 q^{85} - 15004352 q^{86} + 9911300 q^{87} + 73235752 q^{88} - 3586060 q^{89} + 19854300 q^{90} - 6248552 q^{91} + 18332792 q^{92} - 51792248 q^{93} - 39035704 q^{94} + 10879200 q^{95} - 62142208 q^{96} + 21847256 q^{97} - 40577688 q^{98} + 705672 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(60))\)

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
60.8.a \(\chi_{60}(1, \cdot)\) 60.8.a.a 1 1
60.8.a.b 1
60.8.a.c 1
60.8.a.d 1
60.8.d \(\chi_{60}(49, \cdot)\) 60.8.d.a 2 1
60.8.d.b 4
60.8.e \(\chi_{60}(11, \cdot)\) 60.8.e.a 56 1
60.8.h \(\chi_{60}(59, \cdot)\) 60.8.h.a 4 1
60.8.h.b 4
60.8.h.c 72
60.8.i \(\chi_{60}(17, \cdot)\) 60.8.i.a 28 2
60.8.j \(\chi_{60}(7, \cdot)\) 60.8.j.a 84 2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(60))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(60)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)