Properties

Label 117.1
Level 117
Weight 1
Dimension 2
Nonzero newspaces 1
Newforms 1
Sturm bound 1008
Trace bound 0

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Defining parameters

Level: \( N \) = \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(1008\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(117))\).

Total New Old
Modular forms 100 52 48
Cusp forms 4 2 2
Eisenstein series 96 50 46

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - 2q^{7} + O(q^{10}) \) \( 2q - 2q^{7} - 2q^{16} - 2q^{19} + 2q^{28} + 2q^{31} + 2q^{37} + 2q^{52} - 2q^{67} - 2q^{73} - 2q^{76} - 2q^{91} + 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(117))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
117.1.c \(\chi_{117}(53, \cdot)\) None 0 1
117.1.d \(\chi_{117}(116, \cdot)\) None 0 1
117.1.j \(\chi_{117}(73, \cdot)\) 117.1.j.a 2 2
117.1.k \(\chi_{117}(29, \cdot)\) None 0 2
117.1.m \(\chi_{117}(23, \cdot)\) None 0 2
117.1.n \(\chi_{117}(38, \cdot)\) None 0 2
117.1.o \(\chi_{117}(17, \cdot)\) None 0 2
117.1.p \(\chi_{117}(35, \cdot)\) None 0 2
117.1.s \(\chi_{117}(14, \cdot)\) None 0 2
117.1.u \(\chi_{117}(68, \cdot)\) None 0 2
117.1.v \(\chi_{117}(95, \cdot)\) None 0 2
117.1.w \(\chi_{117}(58, \cdot)\) None 0 4
117.1.y \(\chi_{117}(31, \cdot)\) None 0 4
117.1.bb \(\chi_{117}(7, \cdot)\) None 0 4
117.1.bd \(\chi_{117}(19, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(117))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(117)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)