Properties

Label 1859.1
Level 1859
Weight 1
Dimension 56
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 283920
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(283920\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1859))\).

Total New Old
Modular forms 2344 1897 447
Cusp forms 64 56 8
Eisenstein series 2280 1841 439

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 56 0 0 0

Trace form

\( 56 q + 2 q^{3} - 2 q^{4} - 2 q^{9} + O(q^{10}) \) \( 56 q + 2 q^{3} - 2 q^{4} - 2 q^{9} + 6 q^{12} - 20 q^{14} + 2 q^{22} + 2 q^{23} - 4 q^{25} - 44 q^{27} - 6 q^{36} - 6 q^{38} - 2 q^{42} - 2 q^{49} - 22 q^{53} - 2 q^{56} + 2 q^{64} + 30 q^{66} + 4 q^{69} + 2 q^{75} + 2 q^{77} + 4 q^{82} + 4 q^{88} + 8 q^{92} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1859))\)

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
1859.1.c \(\chi_{1859}(846, \cdot)\) 1859.1.c.a 3 1
1859.1.c.b 3
1859.1.c.c 4
1859.1.d \(\chi_{1859}(1858, \cdot)\) 1859.1.d.a 6 1
1859.1.f \(\chi_{1859}(408, \cdot)\) None 0 2
1859.1.i \(\chi_{1859}(868, \cdot)\) 1859.1.i.a 4 2
1859.1.i.b 4
1859.1.i.c 12
1859.1.k \(\chi_{1859}(1374, \cdot)\) 1859.1.k.a 6 2
1859.1.k.b 6
1859.1.k.c 8
1859.1.l \(\chi_{1859}(337, \cdot)\) None 0 4
1859.1.m \(\chi_{1859}(508, \cdot)\) None 0 4
1859.1.p \(\chi_{1859}(89, \cdot)\) None 0 4
1859.1.s \(\chi_{1859}(70, \cdot)\) None 0 8
1859.1.u \(\chi_{1859}(142, \cdot)\) None 0 12
1859.1.v \(\chi_{1859}(131, \cdot)\) None 0 12
1859.1.x \(\chi_{1859}(315, \cdot)\) None 0 8
1859.1.z \(\chi_{1859}(316, \cdot)\) None 0 8
1859.1.bc \(\chi_{1859}(34, \cdot)\) None 0 24
1859.1.be \(\chi_{1859}(80, \cdot)\) None 0 16
1859.1.bg \(\chi_{1859}(87, \cdot)\) None 0 24
1859.1.bi \(\chi_{1859}(10, \cdot)\) None 0 24
1859.1.bk \(\chi_{1859}(40, \cdot)\) None 0 48
1859.1.bl \(\chi_{1859}(51, \cdot)\) None 0 48
1859.1.bm \(\chi_{1859}(45, \cdot)\) None 0 48
1859.1.bq \(\chi_{1859}(5, \cdot)\) None 0 96
1859.1.br \(\chi_{1859}(17, \cdot)\) None 0 96
1859.1.bt \(\chi_{1859}(29, \cdot)\) None 0 96
1859.1.bu \(\chi_{1859}(15, \cdot)\) None 0 192

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1859))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1859)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 2}\)