Properties

Label 6.5
Level 6
Weight 5
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(6))\).

Total New Old
Modular forms 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

Trace form

\( 2 q - 6 q^{3} - 16 q^{4} + 48 q^{6} + 52 q^{7} - 126 q^{9} + O(q^{10}) \) \( 2 q - 6 q^{3} - 16 q^{4} + 48 q^{6} + 52 q^{7} - 126 q^{9} - 96 q^{10} + 48 q^{12} + 100 q^{13} + 288 q^{15} + 128 q^{16} - 288 q^{18} - 716 q^{19} - 156 q^{21} + 672 q^{22} - 384 q^{24} + 674 q^{25} + 1242 q^{27} - 416 q^{28} + 288 q^{30} - 1484 q^{31} - 2016 q^{33} - 1152 q^{34} + 1008 q^{36} + 3748 q^{37} - 300 q^{39} + 768 q^{40} + 1248 q^{42} - 524 q^{43} - 1728 q^{45} - 2112 q^{46} - 384 q^{48} - 3450 q^{49} + 3456 q^{51} - 800 q^{52} - 2160 q^{54} + 4032 q^{55} + 2148 q^{57} + 8160 q^{58} - 2304 q^{60} - 2972 q^{61} - 3276 q^{63} - 1024 q^{64} - 2016 q^{66} - 8972 q^{67} + 6336 q^{69} - 2496 q^{70} + 2304 q^{72} + 580 q^{73} - 2022 q^{75} + 5728 q^{76} + 2400 q^{78} + 19636 q^{79} + 2754 q^{81} - 13632 q^{82} + 1248 q^{84} - 6912 q^{85} - 24480 q^{87} - 5376 q^{88} + 6048 q^{90} + 2600 q^{91} + 4452 q^{93} + 9600 q^{94} + 3072 q^{96} - 956 q^{97} + 12096 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)

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
6.5.b \(\chi_{6}(5, \cdot)\) 6.5.b.a 2 1