Properties

Label 14.10
Level 14
Weight 10
Dimension 16
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 120
Trace bound 1

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(14))\).

Total New Old
Modular forms 60 16 44
Cusp forms 48 16 32
Eisenstein series 12 0 12

Trace form

\( 16 q - 32 q^{2} - 12 q^{3} - 512 q^{4} - 3444 q^{5} + 12768 q^{6} - 1784 q^{7} - 8192 q^{8} + 41388 q^{9} + 49056 q^{10} + 49506 q^{11} - 3072 q^{12} + 204410 q^{13} - 175904 q^{14} + 624372 q^{15} - 131072 q^{16}+ \cdots - 981228444 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(14))\)

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
14.10.a \(\chi_{14}(1, \cdot)\) 14.10.a.a 1 1
14.10.a.b 1
14.10.a.c 2
14.10.c \(\chi_{14}(9, \cdot)\) 14.10.c.a 6 2
14.10.c.b 6

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)