Properties

Label 10.20
Level 10
Weight 20
Dimension 15
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 120
Trace bound 1

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 20 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_1(10))\).

Total New Old
Modular forms 61 15 46
Cusp forms 53 15 38
Eisenstein series 8 0 8

Trace form

\( 15 q + 512 q^{2} + 70372 q^{3} - 1310720 q^{4} + 4855795 q^{5} + 46888960 q^{6} - 272909624 q^{7} + 134217728 q^{8} - 8812644985 q^{9} + 997470720 q^{10} - 26607658820 q^{11} + 18447597568 q^{12} + 42687059302 q^{13}+ \cdots + 68\!\cdots\!80 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.20.a \(\chi_{10}(1, \cdot)\) 10.20.a.a 1 1
10.20.a.b 1
10.20.a.c 1
10.20.a.d 2
10.20.b \(\chi_{10}(9, \cdot)\) 10.20.b.a 10 1

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)