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Properties

Label 1564.1
Level 1564
Weight 1
Dimension 40
Nonzero newspaces 1
Newform subspaces 3
Sturm bound 152064
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1564 = 2^{2} \cdot 17 \cdot 23 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 3 \)
Sturm bound: \(152064\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1564))\).

Total New Old
Modular forms 1830 672 1158
Cusp forms 70 40 30
Eisenstein series 1760 632 1128

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 40 0 0 0

Trace form

\( 40 q - 4 q^{4} - 4 q^{9} + O(q^{10}) \) \( 40 q - 4 q^{4} - 4 q^{9} - 4 q^{16} - 4 q^{17} - 8 q^{18} - 8 q^{21} - 4 q^{25} - 8 q^{26} - 8 q^{33} - 4 q^{36} - 8 q^{42} - 4 q^{49} - 8 q^{53} - 4 q^{64} - 8 q^{66} + 40 q^{68} - 4 q^{69} + 36 q^{72} - 8 q^{77} - 12 q^{81} - 8 q^{84} - 8 q^{93} - 8 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1564))\)

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
1564.1.d \(\chi_{1564}(783, \cdot)\) None 0 1
1564.1.e \(\chi_{1564}(781, \cdot)\) None 0 1
1564.1.f \(\chi_{1564}(137, \cdot)\) None 0 1
1564.1.g \(\chi_{1564}(1427, \cdot)\) None 0 1
1564.1.k \(\chi_{1564}(965, \cdot)\) None 0 2
1564.1.l \(\chi_{1564}(47, \cdot)\) None 0 2
1564.1.m \(\chi_{1564}(875, \cdot)\) None 0 4
1564.1.p \(\chi_{1564}(229, \cdot)\) None 0 4
1564.1.s \(\chi_{1564}(277, \cdot)\) None 0 8
1564.1.t \(\chi_{1564}(91, \cdot)\) None 0 8
1564.1.w \(\chi_{1564}(271, \cdot)\) 1564.1.w.a 10 10
1564.1.w.b 10
1564.1.w.c 20
1564.1.x \(\chi_{1564}(205, \cdot)\) None 0 10
1564.1.y \(\chi_{1564}(33, \cdot)\) None 0 10
1564.1.z \(\chi_{1564}(35, \cdot)\) None 0 10
1564.1.bc \(\chi_{1564}(55, \cdot)\) None 0 20
1564.1.bd \(\chi_{1564}(21, \cdot)\) None 0 20
1564.1.bg \(\chi_{1564}(53, \cdot)\) None 0 40
1564.1.bj \(\chi_{1564}(59, \cdot)\) None 0 40
1564.1.bl \(\chi_{1564}(7, \cdot)\) None 0 80
1564.1.bm \(\chi_{1564}(29, \cdot)\) None 0 80

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1564))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1564)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(391))\)\(^{\oplus 3}\)