Properties

Label 19.5
Level 19
Weight 5
Dimension 51
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 150
Trace bound 1

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(150\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(19))\).

Total New Old
Modular forms 69 69 0
Cusp forms 51 51 0
Eisenstein series 18 18 0

Trace form

\( 51 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} - 9 q^{10} - 9 q^{11} + 855 q^{12} - 69 q^{13} - 873 q^{14} - 1143 q^{15} - 2025 q^{16} - 306 q^{17} + 768 q^{19} + 2574 q^{20}+ \cdots + 60507 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(19))\)

We only show spaces with odd 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
19.5.b \(\chi_{19}(18, \cdot)\) 19.5.b.a 1 1
19.5.b.b 4
19.5.d \(\chi_{19}(8, \cdot)\) 19.5.d.a 10 2
19.5.f \(\chi_{19}(2, \cdot)\) 19.5.f.a 36 6