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Properties

Label 62.6
Level 62
Weight 6
Dimension 200
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 1440
Trace bound 1

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Defining parameters

Level: \( N \) = \( 62 = 2 \cdot 31 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(1440\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(62))\).

Total New Old
Modular forms 630 200 430
Cusp forms 570 200 370
Eisenstein series 60 0 60

Trace form

\( 200 q + 18990 q^{21} + 10680 q^{22} - 13530 q^{23} - 43750 q^{25} - 9480 q^{26} + 7290 q^{27} + 18560 q^{28} + 45300 q^{29} + 54000 q^{30} + 52140 q^{31} + 16740 q^{33} - 13200 q^{34} - 46500 q^{35} - 51840 q^{36}+ \cdots - 352650 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(62))\)

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
62.6.a \(\chi_{62}(1, \cdot)\) 62.6.a.a 2 1
62.6.a.b 2
62.6.a.c 4
62.6.a.d 4
62.6.c \(\chi_{62}(5, \cdot)\) 62.6.c.a 14 2
62.6.c.b 14
62.6.d \(\chi_{62}(33, \cdot)\) 62.6.d.a 24 4
62.6.d.b 24
62.6.g \(\chi_{62}(7, \cdot)\) 62.6.g.a 56 8
62.6.g.b 56

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(62))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(62)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)