Properties

Label 48.3
Level 48
Weight 3
Dimension 49
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 384
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(384\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(48))\).

Total New Old
Modular forms 156 59 97
Cusp forms 100 49 51
Eisenstein series 56 10 46

Trace form

\( 49 q - q^{3} + 8 q^{4} + 12 q^{5} + 4 q^{6} + 10 q^{7} - 12 q^{8} - 11 q^{9} - 80 q^{10} + 32 q^{11} - 56 q^{12} - 34 q^{13} - 44 q^{14} - 36 q^{15} + 16 q^{16} - 12 q^{17} - 48 q^{18} - 98 q^{19} + 80 q^{20}+ \cdots - 260 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.3.b \(\chi_{48}(7, \cdot)\) None 0 1
48.3.e \(\chi_{48}(17, \cdot)\) 48.3.e.a 1 1
48.3.e.b 2
48.3.g \(\chi_{48}(31, \cdot)\) 48.3.g.a 2 1
48.3.h \(\chi_{48}(41, \cdot)\) None 0 1
48.3.i \(\chi_{48}(5, \cdot)\) 48.3.i.a 8 2
48.3.i.b 20
48.3.l \(\chi_{48}(19, \cdot)\) 48.3.l.a 16 2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

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