Properties

Label 185.2
Level 185
Weight 2
Dimension 1145
Nonzero newspaces 18
Newform subspaces 31
Sturm bound 5472
Trace bound 3

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Defining parameters

Level: \( N \) = \( 185 = 5 \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Newform subspaces: \( 31 \)
Sturm bound: \(5472\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(185))\).

Total New Old
Modular forms 1512 1357 155
Cusp forms 1225 1145 80
Eisenstein series 287 212 75

Trace form

\( 1145 q - 39 q^{2} - 40 q^{3} - 43 q^{4} - 55 q^{5} - 120 q^{6} - 44 q^{7} - 51 q^{8} - 49 q^{9} - 57 q^{10} - 120 q^{11} - 64 q^{12} - 50 q^{13} - 60 q^{14} - 58 q^{15} - 139 q^{16} - 54 q^{17} - 75 q^{18}+ \cdots - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)

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
185.2.a \(\chi_{185}(1, \cdot)\) 185.2.a.a 1 1
185.2.a.b 1
185.2.a.c 1
185.2.a.d 5
185.2.a.e 5
185.2.b \(\chi_{185}(149, \cdot)\) 185.2.b.a 18 1
185.2.c \(\chi_{185}(36, \cdot)\) 185.2.c.a 2 1
185.2.c.b 12
185.2.d \(\chi_{185}(184, \cdot)\) 185.2.d.a 16 1
185.2.e \(\chi_{185}(26, \cdot)\) 185.2.e.a 14 2
185.2.e.b 14
185.2.f \(\chi_{185}(43, \cdot)\) 185.2.f.a 2 2
185.2.f.b 2
185.2.f.c 6
185.2.f.d 24
185.2.k \(\chi_{185}(68, \cdot)\) 185.2.k.a 2 2
185.2.k.b 2
185.2.k.c 6
185.2.k.d 24
185.2.l \(\chi_{185}(64, \cdot)\) 185.2.l.a 32 2
185.2.m \(\chi_{185}(11, \cdot)\) 185.2.m.a 28 2
185.2.n \(\chi_{185}(84, \cdot)\) 185.2.n.a 36 2
185.2.o \(\chi_{185}(16, \cdot)\) 185.2.o.a 36 6
185.2.o.b 36
185.2.p \(\chi_{185}(82, \cdot)\) 185.2.p.a 68 4
185.2.u \(\chi_{185}(8, \cdot)\) 185.2.u.a 68 4
185.2.v \(\chi_{185}(4, \cdot)\) 185.2.v.a 96 6
185.2.w \(\chi_{185}(21, \cdot)\) 185.2.w.a 72 6
185.2.x \(\chi_{185}(9, \cdot)\) 185.2.x.a 108 6
185.2.z \(\chi_{185}(17, \cdot)\) 185.2.z.a 204 12
185.2.bc \(\chi_{185}(2, \cdot)\) 185.2.bc.a 204 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(185))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(185)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 2}\)