Properties

Label 117.3
Level 117
Weight 3
Dimension 740
Nonzero newspaces 15
Newform subspaces 21
Sturm bound 3024
Trace bound 4

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Defining parameters

Level: \( N \) = \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 15 \)
Newform subspaces: \( 21 \)
Sturm bound: \(3024\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(117))\).

Total New Old
Modular forms 1104 840 264
Cusp forms 912 740 172
Eisenstein series 192 100 92

Trace form

\( 740 q - 12 q^{2} - 18 q^{3} - 16 q^{4} - 30 q^{5} - 42 q^{6} - 4 q^{7} + 18 q^{8} - 6 q^{9} - 6 q^{11} - 36 q^{12} - 34 q^{13} - 72 q^{14} - 24 q^{15} - 120 q^{16} - 24 q^{17} - 24 q^{18} - 82 q^{19} + 42 q^{20}+ \cdots + 1200 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(117))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
117.3.c \(\chi_{117}(53, \cdot)\) 117.3.c.a 8 1
117.3.d \(\chi_{117}(116, \cdot)\) 117.3.d.a 8 1
117.3.j \(\chi_{117}(73, \cdot)\) 117.3.j.a 4 2
117.3.j.b 8
117.3.j.c 8
117.3.k \(\chi_{117}(29, \cdot)\) 117.3.k.a 52 2
117.3.m \(\chi_{117}(23, \cdot)\) 117.3.m.a 52 2
117.3.n \(\chi_{117}(38, \cdot)\) 117.3.n.a 52 2
117.3.o \(\chi_{117}(17, \cdot)\) 117.3.o.a 20 2
117.3.p \(\chi_{117}(35, \cdot)\) 117.3.p.a 20 2
117.3.s \(\chi_{117}(14, \cdot)\) 117.3.s.a 48 2
117.3.u \(\chi_{117}(68, \cdot)\) 117.3.u.a 52 2
117.3.v \(\chi_{117}(95, \cdot)\) 117.3.v.a 52 2
117.3.w \(\chi_{117}(58, \cdot)\) 117.3.w.a 104 4
117.3.y \(\chi_{117}(31, \cdot)\) 117.3.y.a 104 4
117.3.bb \(\chi_{117}(7, \cdot)\) 117.3.bb.a 104 4
117.3.bd \(\chi_{117}(19, \cdot)\) 117.3.bd.a 4 4
117.3.bd.b 4
117.3.bd.c 8
117.3.bd.d 12
117.3.bd.e 16

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(117))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(117)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 1}\)