Properties

Label 25.4
Level 25
Weight 4
Dimension 59
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 200
Trace bound 1

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 7 \)
Sturm bound: \(200\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(25))\).

Total New Old
Modular forms 89 80 9
Cusp forms 61 59 2
Eisenstein series 28 21 7

Trace form

\( 59 q - 2 q^{2} - 14 q^{3} - 26 q^{4} - 5 q^{5} - 2 q^{6} - 22 q^{7} - 10 q^{8} + 36 q^{9} - 30 q^{10} - 82 q^{11} - 42 q^{12} + 66 q^{13} + 38 q^{14} - 146 q^{16} - 382 q^{17} - 644 q^{18} - 330 q^{19}+ \cdots + 13332 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.4.a \(\chi_{25}(1, \cdot)\) 25.4.a.a 1 1
25.4.a.b 1
25.4.a.c 1
25.4.b \(\chi_{25}(24, \cdot)\) 25.4.b.a 2 1
25.4.b.b 2
25.4.d \(\chi_{25}(6, \cdot)\) 25.4.d.a 28 4
25.4.e \(\chi_{25}(4, \cdot)\) 25.4.e.a 24 4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)