Properties

Label 48.8
Level 48
Weight 8
Dimension 185
Nonzero newspaces 4
Newform subspaces 12
Sturm bound 1024
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 12 \)
Sturm bound: \(1024\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(48))\).

Total New Old
Modular forms 476 193 283
Cusp forms 420 185 235
Eisenstein series 56 8 48

Trace form

\( 185 q - 29 q^{3} + 360 q^{4} - 278 q^{5} + 172 q^{6} - 328 q^{7} + 2004 q^{8} + 1749 q^{9} - 25952 q^{10} - 3612 q^{11} + 27352 q^{12} + 3018 q^{13} - 44028 q^{14} + 33750 q^{15} - 52784 q^{16} + 1454 q^{17}+ \cdots - 7334224 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.8.a \(\chi_{48}(1, \cdot)\) 48.8.a.a 1 1
48.8.a.b 1
48.8.a.c 1
48.8.a.d 1
48.8.a.e 1
48.8.a.f 1
48.8.a.g 1
48.8.c \(\chi_{48}(47, \cdot)\) 48.8.c.a 2 1
48.8.c.b 4
48.8.c.c 8
48.8.d \(\chi_{48}(25, \cdot)\) None 0 1
48.8.f \(\chi_{48}(23, \cdot)\) None 0 1
48.8.j \(\chi_{48}(13, \cdot)\) 48.8.j.a 56 2
48.8.k \(\chi_{48}(11, \cdot)\) 48.8.k.a 108 2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)