Properties

Label 737.1
Level 737
Weight 1
Dimension 32
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 44880
Trace bound 1

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Defining parameters

Level: \( N \) = \( 737 = 11 \cdot 67 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(44880\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(737))\).

Total New Old
Modular forms 692 616 76
Cusp forms 32 32 0
Eisenstein series 660 584 76

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 32 0 0 0

Trace form

\( 32 q - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{9} + O(q^{10}) \) \( 32 q - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{9} - q^{11} - 2 q^{12} - 4 q^{15} - q^{16} - 2 q^{20} - 2 q^{23} - 3 q^{25} - 4 q^{27} - 2 q^{31} - 2 q^{33} - 3 q^{36} - 2 q^{37} - q^{44} - 6 q^{45} - 2 q^{47} - 2 q^{48} - q^{49} - 2 q^{53} + 31 q^{55} - 2 q^{59} - 4 q^{60} - q^{64} - q^{67} - 4 q^{69} - 2 q^{71} - 6 q^{75} - 2 q^{80} + 28 q^{81} - 2 q^{89} - 2 q^{92} - 4 q^{93} - 2 q^{97} - 3 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(737))\)

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
737.1.b \(\chi_{737}(133, \cdot)\) None 0 1
737.1.c \(\chi_{737}(604, \cdot)\) None 0 1
737.1.h \(\chi_{737}(298, \cdot)\) None 0 2
737.1.i \(\chi_{737}(230, \cdot)\) 737.1.i.a 2 2
737.1.k \(\chi_{737}(68, \cdot)\) None 0 4
737.1.l \(\chi_{737}(267, \cdot)\) None 0 4
737.1.p \(\chi_{737}(76, \cdot)\) 737.1.p.a 10 10
737.1.q \(\chi_{737}(45, \cdot)\) None 0 10
737.1.r \(\chi_{737}(29, \cdot)\) None 0 8
737.1.s \(\chi_{737}(38, \cdot)\) None 0 8
737.1.w \(\chi_{737}(10, \cdot)\) 737.1.w.a 20 20
737.1.x \(\chi_{737}(12, \cdot)\) None 0 20
737.1.z \(\chi_{737}(3, \cdot)\) None 0 40
737.1.ba \(\chi_{737}(24, \cdot)\) None 0 40
737.1.be \(\chi_{737}(20, \cdot)\) None 0 80
737.1.bf \(\chi_{737}(6, \cdot)\) None 0 80