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Properties

Label 123.4
Level 123
Weight 4
Dimension 1220
Nonzero newspaces 8
Newform subspaces 12
Sturm bound 4480
Trace bound 5

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Defining parameters

Level: \( N \) = \( 123 = 3 \cdot 41 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 12 \)
Sturm bound: \(4480\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(123))\).

Total New Old
Modular forms 1760 1300 460
Cusp forms 1600 1220 380
Eisenstein series 160 80 80

Trace form

\( 1220 q - 20 q^{3} - 40 q^{4} - 20 q^{6} - 40 q^{7} - 20 q^{9} - 40 q^{10} - 20 q^{12} - 40 q^{13} - 20 q^{15} - 40 q^{16} - 20 q^{18} - 40 q^{19} - 20 q^{21} - 40 q^{22} - 20 q^{24} - 40 q^{25} - 20 q^{27}+ \cdots - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(123))\)

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
123.4.a \(\chi_{123}(1, \cdot)\) 123.4.a.a 4 1
123.4.a.b 4
123.4.a.c 6
123.4.a.d 6
123.4.d \(\chi_{123}(40, \cdot)\) 123.4.d.a 20 1
123.4.e \(\chi_{123}(73, \cdot)\) 123.4.e.a 44 2
123.4.g \(\chi_{123}(10, \cdot)\) 123.4.g.a 40 4
123.4.g.b 40
123.4.i \(\chi_{123}(14, \cdot)\) 123.4.i.a 160 4
123.4.j \(\chi_{123}(4, \cdot)\) 123.4.j.a 80 4
123.4.n \(\chi_{123}(43, \cdot)\) 123.4.n.a 176 8
123.4.o \(\chi_{123}(11, \cdot)\) 123.4.o.a 640 16

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(123))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(123)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 2}\)