Properties

Label 351.1
Level 351
Weight 1
Dimension 12
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 9072
Trace bound 4

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Defining parameters

Level: \( N \) = \( 351 = 3^{3} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(9072\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(351))\).

Total New Old
Modular forms 379 188 191
Cusp forms 19 12 7
Eisenstein series 360 176 184

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q + 4 q^{4} + O(q^{10}) \) \( 12 q + 4 q^{4} - 4 q^{10} - 4 q^{22} + 4 q^{25} - 4 q^{28} - 4 q^{31} - 4 q^{37} - 8 q^{40} - 8 q^{43} - 8 q^{52} - 4 q^{55} - 4 q^{82} + 4 q^{88} + 8 q^{94} + 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(351))\)

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
351.1.c \(\chi_{351}(53, \cdot)\) None 0 1
351.1.d \(\chi_{351}(350, \cdot)\) 351.1.d.a 1 1
351.1.d.b 1
351.1.d.c 2
351.1.j \(\chi_{351}(109, \cdot)\) None 0 2
351.1.k \(\chi_{351}(152, \cdot)\) None 0 2
351.1.m \(\chi_{351}(179, \cdot)\) None 0 2
351.1.n \(\chi_{351}(116, \cdot)\) None 0 2
351.1.o \(\chi_{351}(134, \cdot)\) 351.1.o.a 2 2
351.1.p \(\chi_{351}(107, \cdot)\) 351.1.p.a 2 2
351.1.s \(\chi_{351}(170, \cdot)\) None 0 2
351.1.u \(\chi_{351}(35, \cdot)\) None 0 2
351.1.v \(\chi_{351}(17, \cdot)\) None 0 2
351.1.z \(\chi_{351}(154, \cdot)\) None 0 4
351.1.bb \(\chi_{351}(73, \cdot)\) None 0 4
351.1.be \(\chi_{351}(19, \cdot)\) None 0 4
351.1.bg \(\chi_{351}(28, \cdot)\) 351.1.bg.a 4 4
351.1.bh \(\chi_{351}(95, \cdot)\) None 0 6
351.1.bi \(\chi_{351}(38, \cdot)\) None 0 6
351.1.bj \(\chi_{351}(23, \cdot)\) None 0 6
351.1.bk \(\chi_{351}(29, \cdot)\) None 0 6
351.1.bm \(\chi_{351}(14, \cdot)\) None 0 6
351.1.bp \(\chi_{351}(68, \cdot)\) None 0 6
351.1.br \(\chi_{351}(7, \cdot)\) None 0 12
351.1.bs \(\chi_{351}(58, \cdot)\) None 0 12
351.1.bu \(\chi_{351}(31, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(351))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(351)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)