Properties

Label 1183.1
Level 1183
Weight 1
Dimension 60
Nonzero newspaces 7
Newform subspaces 9
Sturm bound 113568
Trace bound 16

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Defining parameters

Level: \( N \) = \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 9 \)
Sturm bound: \(113568\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1183))\).

Total New Old
Modular forms 1428 1083 345
Cusp forms 60 60 0
Eisenstein series 1368 1023 345

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 36 24 0 0

Trace form

\( 60q + O(q^{10}) \) \( 60q - 24q^{14} - 24q^{27} + 12q^{40} - 24q^{53} + 12q^{66} - 36q^{92} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1183))\)

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
1183.1.b \(\chi_{1183}(1182, \cdot)\) 1183.1.b.a 6 1
1183.1.d \(\chi_{1183}(846, \cdot)\) 1183.1.d.a 3 1
1183.1.d.b 3
1183.1.j \(\chi_{1183}(99, \cdot)\) None 0 2
1183.1.l \(\chi_{1183}(530, \cdot)\) None 0 2
1183.1.m \(\chi_{1183}(698, \cdot)\) None 0 2
1183.1.n \(\chi_{1183}(146, \cdot)\) 1183.1.n.a 6 2
1183.1.n.b 6
1183.1.o \(\chi_{1183}(339, \cdot)\) None 0 2
1183.1.p \(\chi_{1183}(192, \cdot)\) None 0 2
1183.1.s \(\chi_{1183}(675, \cdot)\) None 0 2
1183.1.t \(\chi_{1183}(699, \cdot)\) 1183.1.t.a 12 2
1183.1.v \(\chi_{1183}(360, \cdot)\) None 0 2
1183.1.x \(\chi_{1183}(319, \cdot)\) 1183.1.x.a 8 4
1183.1.y \(\chi_{1183}(526, \cdot)\) None 0 4
1183.1.z \(\chi_{1183}(268, \cdot)\) 1183.1.z.a 8 4
1183.1.bd \(\chi_{1183}(249, \cdot)\) 1183.1.bd.a 8 4
1183.1.bf \(\chi_{1183}(27, \cdot)\) None 0 12
1183.1.bh \(\chi_{1183}(90, \cdot)\) None 0 12
1183.1.bm \(\chi_{1183}(8, \cdot)\) None 0 24
1183.1.bo \(\chi_{1183}(68, \cdot)\) None 0 24
1183.1.bq \(\chi_{1183}(62, \cdot)\) None 0 24
1183.1.br \(\chi_{1183}(12, \cdot)\) None 0 24
1183.1.bu \(\chi_{1183}(10, \cdot)\) None 0 24
1183.1.bv \(\chi_{1183}(40, \cdot)\) None 0 24
1183.1.bw \(\chi_{1183}(48, \cdot)\) None 0 24
1183.1.bx \(\chi_{1183}(3, \cdot)\) None 0 24
1183.1.by \(\chi_{1183}(17, \cdot)\) None 0 24
1183.1.ca \(\chi_{1183}(11, \cdot)\) None 0 48
1183.1.ce \(\chi_{1183}(18, \cdot)\) None 0 48
1183.1.cf \(\chi_{1183}(15, \cdot)\) None 0 48
1183.1.cg \(\chi_{1183}(2, \cdot)\) None 0 48