Properties

Label 312.1
Level 312
Weight 1
Dimension 4
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 5376
Trace bound 0

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Defining parameters

Level: \( N \) = \( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(5376\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(312))\).

Total New Old
Modular forms 316 48 268
Cusp forms 28 4 24
Eisenstein series 288 44 244

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4q - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{9} - 4q^{10} + 4q^{12} - 4q^{16} + 4q^{22} - 4q^{25} + 4q^{30} - 4q^{39} - 4q^{40} + 4q^{49} + 4q^{52} + 8q^{55} - 4q^{66} + 4q^{81} - 4q^{82} + 4q^{88} + 4q^{90} - 4q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(312))\)

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
312.1.b \(\chi_{312}(77, \cdot)\) 312.1.b.a 4 1
312.1.e \(\chi_{312}(235, \cdot)\) None 0 1
312.1.f \(\chi_{312}(209, \cdot)\) None 0 1
312.1.i \(\chi_{312}(103, \cdot)\) None 0 1
312.1.k \(\chi_{312}(79, \cdot)\) None 0 1
312.1.l \(\chi_{312}(233, \cdot)\) None 0 1
312.1.o \(\chi_{312}(259, \cdot)\) None 0 1
312.1.p \(\chi_{312}(53, \cdot)\) None 0 1
312.1.r \(\chi_{312}(109, \cdot)\) None 0 2
312.1.s \(\chi_{312}(73, \cdot)\) None 0 2
312.1.v \(\chi_{312}(47, \cdot)\) None 0 2
312.1.w \(\chi_{312}(83, \cdot)\) None 0 2
312.1.z \(\chi_{312}(127, \cdot)\) None 0 2
312.1.bc \(\chi_{312}(113, \cdot)\) None 0 2
312.1.bd \(\chi_{312}(139, \cdot)\) None 0 2
312.1.bg \(\chi_{312}(101, \cdot)\) None 0 2
312.1.bh \(\chi_{312}(29, \cdot)\) None 0 2
312.1.bi \(\chi_{312}(43, \cdot)\) None 0 2
312.1.bl \(\chi_{312}(17, \cdot)\) None 0 2
312.1.bm \(\chi_{312}(55, \cdot)\) None 0 2
312.1.bq \(\chi_{312}(11, \cdot)\) None 0 4
312.1.br \(\chi_{312}(71, \cdot)\) None 0 4
312.1.bu \(\chi_{312}(97, \cdot)\) None 0 4
312.1.bv \(\chi_{312}(37, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(312))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(312)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 2}\)