Properties

Label 112.4
Level 112
Weight 4
Dimension 599
Nonzero newspaces 8
Newform subspaces 29
Sturm bound 3072
Trace bound 3

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Defining parameters

Level: \( N \) = \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 29 \)
Sturm bound: \(3072\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(112))\).

Total New Old
Modular forms 1236 643 593
Cusp forms 1068 599 469
Eisenstein series 168 44 124

Trace form

\( 599 q - 8 q^{2} - 13 q^{3} - 28 q^{4} - 7 q^{5} + 52 q^{6} + 15 q^{7} + 64 q^{8} + 19 q^{9} + 124 q^{10} - 133 q^{11} - 212 q^{12} - 58 q^{13} - 200 q^{14} + 246 q^{15} - 572 q^{16} - 119 q^{17} - 360 q^{18}+ \cdots - 7868 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(112))\)

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
112.4.a \(\chi_{112}(1, \cdot)\) 112.4.a.a 1 1
112.4.a.b 1
112.4.a.c 1
112.4.a.d 1
112.4.a.e 1
112.4.a.f 1
112.4.a.g 1
112.4.a.h 2
112.4.b \(\chi_{112}(57, \cdot)\) None 0 1
112.4.e \(\chi_{112}(55, \cdot)\) None 0 1
112.4.f \(\chi_{112}(111, \cdot)\) 112.4.f.a 4 1
112.4.f.b 8
112.4.i \(\chi_{112}(65, \cdot)\) 112.4.i.a 2 2
112.4.i.b 2
112.4.i.c 2
112.4.i.d 4
112.4.i.e 6
112.4.i.f 6
112.4.j \(\chi_{112}(27, \cdot)\) 112.4.j.a 4 2
112.4.j.b 88
112.4.m \(\chi_{112}(29, \cdot)\) 112.4.m.a 34 2
112.4.m.b 38
112.4.p \(\chi_{112}(31, \cdot)\) 112.4.p.a 2 2
112.4.p.b 2
112.4.p.c 2
112.4.p.d 2
112.4.p.e 4
112.4.p.f 6
112.4.p.g 6
112.4.q \(\chi_{112}(87, \cdot)\) None 0 2
112.4.t \(\chi_{112}(9, \cdot)\) None 0 2
112.4.v \(\chi_{112}(3, \cdot)\) 112.4.v.a 184 4
112.4.w \(\chi_{112}(37, \cdot)\) 112.4.w.a 184 4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(112)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)