Properties

Label 112.6
Level 112
Weight 6
Dimension 1013
Nonzero newspaces 8
Sturm bound 4608
Trace bound 3

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Defining parameters

Level: \( N \) = \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(4608\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(112))\).

Total New Old
Modular forms 2004 1057 947
Cusp forms 1836 1013 823
Eisenstein series 168 44 124

Trace form

\( 1013 q - 8 q^{2} + 11 q^{3} + 36 q^{4} + 29 q^{5} - 236 q^{6} - 121 q^{7} - 512 q^{8} - 119 q^{9} + 860 q^{10} + 2531 q^{11} - 20 q^{12} - 134 q^{13} + 88 q^{14} - 7866 q^{15} + 1732 q^{16} + 1189 q^{17}+ \cdots - 1284092 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(112))\)

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
112.6.a \(\chi_{112}(1, \cdot)\) 112.6.a.a 1 1
112.6.a.b 1
112.6.a.c 1
112.6.a.d 1
112.6.a.e 1
112.6.a.f 1
112.6.a.g 1
112.6.a.h 2
112.6.a.i 2
112.6.a.j 2
112.6.a.k 2
112.6.b \(\chi_{112}(57, \cdot)\) None 0 1
112.6.e \(\chi_{112}(55, \cdot)\) None 0 1
112.6.f \(\chi_{112}(111, \cdot)\) 112.6.f.a 8 1
112.6.f.b 12
112.6.i \(\chi_{112}(65, \cdot)\) 112.6.i.a 2 2
112.6.i.b 4
112.6.i.c 4
112.6.i.d 4
112.6.i.e 4
112.6.i.f 10
112.6.i.g 10
112.6.j \(\chi_{112}(27, \cdot)\) n/a 156 2
112.6.m \(\chi_{112}(29, \cdot)\) n/a 120 2
112.6.p \(\chi_{112}(31, \cdot)\) 112.6.p.a 12 2
112.6.p.b 14
112.6.p.c 14
112.6.q \(\chi_{112}(87, \cdot)\) None 0 2
112.6.t \(\chi_{112}(9, \cdot)\) None 0 2
112.6.v \(\chi_{112}(3, \cdot)\) n/a 312 4
112.6.w \(\chi_{112}(37, \cdot)\) n/a 312 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces

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