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Properties

Label 943.1
Level 943
Weight 1
Dimension 63
Nonzero newspaces 5
Newform subspaces 12
Sturm bound 73920
Trace bound 6

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Defining parameters

Level: \( N \) = \( 943 = 23 \cdot 41 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 12 \)
Sturm bound: \(73920\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(943))\).

Total New Old
Modular forms 945 881 64
Cusp forms 65 63 2
Eisenstein series 880 818 62

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 63 0 0 0

Trace form

\( 63 q - q^{4} - 6 q^{6} - 6 q^{8} + 3 q^{9} + O(q^{10}) \) \( 63 q - q^{4} - 6 q^{6} - 6 q^{8} + 3 q^{9} - 6 q^{12} - 5 q^{16} - 6 q^{18} - 5 q^{23} - 6 q^{24} + 3 q^{25} - 6 q^{26} - 6 q^{27} - 6 q^{32} - 7 q^{36} - 6 q^{39} - 2 q^{41} - 12 q^{48} + 3 q^{49} - 6 q^{52} - 6 q^{54} - 6 q^{58} - 10 q^{59} - 14 q^{62} - 15 q^{64} + 48 q^{72} - 4 q^{73} - 4 q^{77} - 6 q^{78} + 3 q^{81} - 3 q^{82} - 6 q^{87} - 9 q^{92} - 6 q^{93} + 54 q^{94} - 12 q^{96} - 8 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(943))\)

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
943.1.b \(\chi_{943}(942, \cdot)\) 943.1.b.a 1 1
943.1.b.b 2
943.1.b.c 2
943.1.b.d 4
943.1.d \(\chi_{943}(206, \cdot)\) None 0 1
943.1.f \(\chi_{943}(91, \cdot)\) 943.1.f.a 2 2
943.1.f.b 4
943.1.i \(\chi_{943}(208, \cdot)\) None 0 4
943.1.k \(\chi_{943}(45, \cdot)\) 943.1.k.a 4 4
943.1.k.b 8
943.1.l \(\chi_{943}(160, \cdot)\) 943.1.l.a 4 4
943.1.l.b 8
943.1.n \(\chi_{943}(367, \cdot)\) 943.1.n.a 8 8
943.1.n.b 16
943.1.p \(\chi_{943}(42, \cdot)\) None 0 10
943.1.r \(\chi_{943}(40, \cdot)\) None 0 10
943.1.s \(\chi_{943}(24, \cdot)\) None 0 16
943.1.u \(\chi_{943}(132, \cdot)\) None 0 20
943.1.x \(\chi_{943}(3, \cdot)\) None 0 40
943.1.z \(\chi_{943}(10, \cdot)\) None 0 40
943.1.ba \(\chi_{943}(66, \cdot)\) None 0 40
943.1.bd \(\chi_{943}(5, \cdot)\) None 0 80
943.1.bf \(\chi_{943}(6, \cdot)\) None 0 160

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(943))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(943)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)