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Properties

Label 19.3
Level 19
Weight 3
Dimension 21
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 90
Trace bound 1

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(90\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(19))\).

Total New Old
Modular forms 39 39 0
Cusp forms 21 21 0
Eisenstein series 18 18 0

Trace form

\( 21 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} - 9 q^{10} - 9 q^{11} + 63 q^{12} + 51 q^{13} + 63 q^{14} + 45 q^{15} + 63 q^{16} - 30 q^{19} - 90 q^{20} - 72 q^{21}+ \cdots + 513 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)

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
19.3.b \(\chi_{19}(18, \cdot)\) 19.3.b.a 1 1
19.3.b.b 2
19.3.d \(\chi_{19}(8, \cdot)\) 19.3.d.a 6 2
19.3.f \(\chi_{19}(2, \cdot)\) 19.3.f.a 12 6