Properties

Label 320.1
Level 320
Weight 1
Dimension 3
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 6144
Trace bound 1

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Defining parameters

Level: \( N \) = \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(6144\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(320))\).

Total New Old
Modular forms 298 69 229
Cusp forms 10 3 7
Eisenstein series 288 66 222

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3 q + q^{5} - q^{9} + O(q^{10}) \) \( 3 q + q^{5} - q^{9} + 2 q^{13} - 2 q^{17} - q^{25} - 2 q^{29} - 2 q^{37} - 2 q^{41} - 3 q^{45} - q^{49} - 2 q^{53} + 2 q^{61} + 2 q^{65} + 2 q^{73} - q^{81} + 2 q^{85} + 2 q^{89} + 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(320))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
320.1.b \(\chi_{320}(191, \cdot)\) None 0 1
320.1.e \(\chi_{320}(159, \cdot)\) None 0 1
320.1.g \(\chi_{320}(31, \cdot)\) None 0 1
320.1.h \(\chi_{320}(319, \cdot)\) 320.1.h.a 1 1
320.1.i \(\chi_{320}(177, \cdot)\) None 0 2
320.1.k \(\chi_{320}(79, \cdot)\) None 0 2
320.1.m \(\chi_{320}(33, \cdot)\) None 0 2
320.1.p \(\chi_{320}(193, \cdot)\) 320.1.p.a 2 2
320.1.r \(\chi_{320}(111, \cdot)\) None 0 2
320.1.t \(\chi_{320}(17, \cdot)\) None 0 2
320.1.v \(\chi_{320}(57, \cdot)\) None 0 4
320.1.w \(\chi_{320}(71, \cdot)\) None 0 4
320.1.y \(\chi_{320}(39, \cdot)\) None 0 4
320.1.bb \(\chi_{320}(137, \cdot)\) None 0 4
320.1.bc \(\chi_{320}(53, \cdot)\) None 0 8
320.1.bg \(\chi_{320}(11, \cdot)\) None 0 8
320.1.bh \(\chi_{320}(19, \cdot)\) None 0 8
320.1.bi \(\chi_{320}(13, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(320))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(320)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)