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Properties

Label 15.3
Level 15
Weight 3
Dimension 8
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 48
Trace bound 3

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(15))\).

Total New Old
Modular forms 24 12 12
Cusp forms 8 8 0
Eisenstein series 16 4 12

Trace form

\( 8 q - 4 q^{2} - 4 q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{7} + 12 q^{8} + 16 q^{9} + 24 q^{10} + 16 q^{11} + 28 q^{12} - 16 q^{15} - 48 q^{16} - 40 q^{17} - 52 q^{18} - 48 q^{19} - 36 q^{20} + 40 q^{22}+ \cdots + 80 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)

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
15.3.c \(\chi_{15}(11, \cdot)\) 15.3.c.a 2 1
15.3.d \(\chi_{15}(14, \cdot)\) 15.3.d.a 1 1
15.3.d.b 1
15.3.f \(\chi_{15}(7, \cdot)\) 15.3.f.a 4 2