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Properties

Label 60.5
Level 60
Weight 5
Dimension 150
Nonzero newspaces 6
Newform subspaces 7
Sturm bound 960
Trace bound 5

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Defining parameters

Level: \( N \) = \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 7 \)
Sturm bound: \(960\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(60))\).

Total New Old
Modular forms 424 166 258
Cusp forms 344 150 194
Eisenstein series 80 16 64

Trace form

\( 150 q - 12 q^{2} - 8 q^{3} + 40 q^{4} - 12 q^{5} - 4 q^{6} - 32 q^{7} - 180 q^{8} + 194 q^{9} + O(q^{10}) \) \( 150 q - 12 q^{2} - 8 q^{3} + 40 q^{4} - 12 q^{5} - 4 q^{6} - 32 q^{7} - 180 q^{8} + 194 q^{9} + 472 q^{10} + 288 q^{11} - 164 q^{12} - 132 q^{13} - 840 q^{14} - 194 q^{15} - 80 q^{16} - 1020 q^{17} + 780 q^{18} + 612 q^{19} + 588 q^{20} + 2776 q^{21} + 88 q^{22} + 1320 q^{23} - 2592 q^{24} + 414 q^{25} - 3720 q^{26} - 368 q^{27} - 1304 q^{28} - 5136 q^{29} + 536 q^{30} - 572 q^{31} + 7668 q^{32} - 1048 q^{33} + 7848 q^{34} + 1416 q^{35} - 1880 q^{36} + 11572 q^{37} - 1320 q^{38} - 4408 q^{39} - 4648 q^{40} - 7080 q^{41} - 2440 q^{42} - 2832 q^{43} - 10248 q^{44} - 4304 q^{45} - 20824 q^{46} + 4800 q^{47} - 2636 q^{48} + 114 q^{49} + 12972 q^{50} + 8852 q^{51} + 12784 q^{52} - 1284 q^{53} - 972 q^{54} + 16672 q^{55} + 29568 q^{56} + 1568 q^{57} + 10760 q^{58} - 1520 q^{60} - 26428 q^{61} - 16152 q^{62} - 472 q^{63} - 30200 q^{64} - 16668 q^{65} - 15120 q^{66} - 20672 q^{67} - 12312 q^{68} + 724 q^{69} + 18856 q^{70} - 3600 q^{71} + 10116 q^{72} + 36956 q^{73} + 62352 q^{74} + 2912 q^{75} + 44720 q^{76} - 7656 q^{77} + 9576 q^{78} + 27756 q^{79} - 16548 q^{80} + 35094 q^{81} - 33640 q^{82} + 12720 q^{83} - 6336 q^{84} - 5768 q^{85} - 18384 q^{86} + 13560 q^{87} + 712 q^{88} - 30960 q^{89} - 7104 q^{90} - 4896 q^{91} + 28848 q^{92} - 11840 q^{93} + 54584 q^{94} - 37200 q^{95} + 22832 q^{96} - 76636 q^{97} + 23940 q^{98} - 66880 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(60))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
60.5.b \(\chi_{60}(29, \cdot)\) 60.5.b.a 8 1
60.5.c \(\chi_{60}(31, \cdot)\) 60.5.c.a 16 1
60.5.f \(\chi_{60}(19, \cdot)\) 60.5.f.a 24 1
60.5.g \(\chi_{60}(41, \cdot)\) 60.5.g.a 2 1
60.5.g.b 4
60.5.k \(\chi_{60}(13, \cdot)\) 60.5.k.a 8 2
60.5.l \(\chi_{60}(23, \cdot)\) 60.5.l.a 88 2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(60))\) into lower level spaces

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