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Properties

Label 40.5
Level 40
Weight 5
Dimension 94
Nonzero newspaces 4
Newform subspaces 8
Sturm bound 480
Trace bound 1

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Defining parameters

Level: \( N \) = \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 8 \)
Sturm bound: \(480\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(40))\).

Total New Old
Modular forms 216 106 110
Cusp forms 168 94 74
Eisenstein series 48 12 36

Trace form

\( 94 q - 8 q^{2} + 20 q^{4} + 24 q^{5} + 128 q^{6} - 84 q^{7} - 308 q^{8} - 58 q^{9} + O(q^{10}) \) \( 94 q - 8 q^{2} + 20 q^{4} + 24 q^{5} + 128 q^{6} - 84 q^{7} - 308 q^{8} - 58 q^{9} - 244 q^{10} + 332 q^{11} + 456 q^{12} + 20 q^{13} + 1136 q^{14} + 524 q^{15} + 40 q^{16} + 176 q^{17} - 124 q^{18} - 1412 q^{19} - 304 q^{20} - 208 q^{21} - 1840 q^{22} - 1924 q^{23} - 2488 q^{24} - 3178 q^{25} + 136 q^{26} + 3408 q^{27} + 1800 q^{28} + 4080 q^{30} + 664 q^{31} - 248 q^{32} + 3888 q^{33} - 1388 q^{34} + 3788 q^{35} - 12256 q^{36} + 3580 q^{37} - 5104 q^{38} + 6036 q^{40} - 7788 q^{41} + 14496 q^{42} + 3168 q^{43} + 7808 q^{44} - 9596 q^{45} - 3184 q^{46} - 14404 q^{47} + 520 q^{48} + 946 q^{49} - 2204 q^{50} - 1440 q^{51} + 916 q^{52} + 12060 q^{53} + 17176 q^{54} + 19888 q^{55} + 5776 q^{56} + 22840 q^{57} + 236 q^{58} + 20540 q^{59} - 3240 q^{60} - 8208 q^{61} - 1504 q^{62} - 22396 q^{63} - 14560 q^{64} - 33116 q^{65} - 22928 q^{66} - 36480 q^{67} + 660 q^{68} - 23640 q^{70} - 17192 q^{71} - 34028 q^{72} + 33336 q^{73} - 22084 q^{74} + 23024 q^{75} - 3536 q^{76} + 10320 q^{77} - 3656 q^{78} - 4584 q^{80} - 23754 q^{81} - 1524 q^{82} - 25680 q^{83} + 16480 q^{84} - 36588 q^{85} + 49904 q^{86} + 39992 q^{87} + 77120 q^{88} - 1972 q^{89} + 103196 q^{90} + 84920 q^{91} + 55440 q^{92} + 53040 q^{93} + 3976 q^{94} + 8008 q^{95} + 47632 q^{96} + 25784 q^{97} - 42064 q^{98} - 46596 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(40))\)

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
40.5.b \(\chi_{40}(31, \cdot)\) None 0 1
40.5.e \(\chi_{40}(19, \cdot)\) 40.5.e.a 1 1
40.5.e.b 1
40.5.e.c 20
40.5.g \(\chi_{40}(11, \cdot)\) 40.5.g.a 16 1
40.5.h \(\chi_{40}(39, \cdot)\) None 0 1
40.5.i \(\chi_{40}(13, \cdot)\) 40.5.i.a 44 2
40.5.l \(\chi_{40}(17, \cdot)\) 40.5.l.a 2 2
40.5.l.b 4
40.5.l.c 6

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(40))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(40)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)