Properties

Label 50.12
Level 50
Weight 12
Dimension 253
Nonzero newspaces 4
Newform subspaces 19
Sturm bound 1800
Trace bound 1

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Defining parameters

Level: \( N \) = \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 19 \)
Sturm bound: \(1800\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(50))\).

Total New Old
Modular forms 853 253 600
Cusp forms 797 253 544
Eisenstein series 56 0 56

Trace form

\( 253 q - 64 q^{2} - 2024 q^{3} + 2048 q^{4} - 3655 q^{5} - 5888 q^{6} + 90448 q^{7} - 65536 q^{8} + 319274 q^{9} + 285920 q^{10} - 59864 q^{11} - 2072576 q^{12} + 4382836 q^{13} + 8605184 q^{14} + 161180 q^{15}+ \cdots - 1906016362252 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(50))\)

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
50.12.a \(\chi_{50}(1, \cdot)\) 50.12.a.a 1 1
50.12.a.b 1
50.12.a.c 1
50.12.a.d 1
50.12.a.e 1
50.12.a.f 2
50.12.a.g 2
50.12.a.h 2
50.12.a.i 3
50.12.a.j 3
50.12.b \(\chi_{50}(49, \cdot)\) 50.12.b.a 2 1
50.12.b.b 2
50.12.b.c 2
50.12.b.d 2
50.12.b.e 4
50.12.b.f 4
50.12.d \(\chi_{50}(11, \cdot)\) 50.12.d.a 52 4
50.12.d.b 56
50.12.e \(\chi_{50}(9, \cdot)\) 50.12.e.a 112 4

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(50)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)