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Properties

Label 640.1
Level 640
Weight 1
Dimension 10
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 24576
Trace bound 1

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Defining parameters

Level: \( N \) = \( 640 = 2^{7} \cdot 5 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(24576\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(640))\).

Total New Old
Modular forms 668 154 514
Cusp forms 28 10 18
Eisenstein series 640 144 496

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 0 0 0

Trace form

\( 10 q - 2 q^{9} + O(q^{10}) \) \( 10 q - 2 q^{9} + 4 q^{17} - 6 q^{25} - 4 q^{41} + 2 q^{49} - 8 q^{65} - 4 q^{73} - 6 q^{81} + 4 q^{89} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(640))\)

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
640.1.b \(\chi_{640}(511, \cdot)\) None 0 1
640.1.e \(\chi_{640}(319, \cdot)\) 640.1.e.a 1 1
640.1.e.b 1
640.1.e.c 4
640.1.g \(\chi_{640}(191, \cdot)\) None 0 1
640.1.h \(\chi_{640}(639, \cdot)\) None 0 1
640.1.i \(\chi_{640}(33, \cdot)\) None 0 2
640.1.k \(\chi_{640}(159, \cdot)\) None 0 2
640.1.m \(\chi_{640}(193, \cdot)\) 640.1.m.a 2 2
640.1.m.b 2
640.1.p \(\chi_{640}(257, \cdot)\) None 0 2
640.1.r \(\chi_{640}(31, \cdot)\) None 0 2
640.1.t \(\chi_{640}(353, \cdot)\) None 0 2
640.1.v \(\chi_{640}(177, \cdot)\) None 0 4
640.1.w \(\chi_{640}(111, \cdot)\) None 0 4
640.1.y \(\chi_{640}(79, \cdot)\) None 0 4
640.1.bb \(\chi_{640}(17, \cdot)\) None 0 4
640.1.bc \(\chi_{640}(137, \cdot)\) None 0 8
640.1.bg \(\chi_{640}(71, \cdot)\) None 0 8
640.1.bh \(\chi_{640}(39, \cdot)\) None 0 8
640.1.bi \(\chi_{640}(57, \cdot)\) None 0 8
640.1.bk \(\chi_{640}(13, \cdot)\) None 0 16
640.1.bn \(\chi_{640}(19, \cdot)\) None 0 16
640.1.bp \(\chi_{640}(11, \cdot)\) None 0 16
640.1.bq \(\chi_{640}(53, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(640))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(640)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)