Properties

Label 8.14
Level 8
Weight 14
Dimension 15
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 56
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(56\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(8))\).

Total New Old
Modular forms 29 17 12
Cusp forms 23 15 8
Eisenstein series 6 2 4

Trace form

\( 15 q - 2 q^{2} + 860 q^{3} - 8556 q^{4} + 14146 q^{5} + 58444 q^{6} + 206232 q^{7} + 1076872 q^{8} - 3319093 q^{9} - 7752648 q^{10} + 9989716 q^{11} - 8536664 q^{12} - 3843462 q^{13} + 21101872 q^{14} + 42509064 q^{15}+ \cdots + 42866396476420 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(8))\)

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
8.14.a \(\chi_{8}(1, \cdot)\) 8.14.a.a 1 1
8.14.a.b 2
8.14.b \(\chi_{8}(5, \cdot)\) 8.14.b.a 2 1
8.14.b.b 10

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)