Properties

Label 643.1
Level 643
Weight 1
Dimension 3
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 34454
Trace bound 0

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Defining parameters

Level: \( N \) = \( 643 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(34454\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(643))\).

Total New Old
Modular forms 324 324 0
Cusp forms 3 3 0
Eisenstein series 321 321 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 2 0

Trace form

\( 3 q - q^{4} - 4 q^{6} + q^{7} - q^{9} + O(q^{10}) \) \( 3 q - q^{4} - 4 q^{6} + q^{7} - q^{9} - q^{16} - 4 q^{22} - 3 q^{23} + 3 q^{25} + 4 q^{26} - 3 q^{28} + q^{29} - 3 q^{31} - 4 q^{33} + 4 q^{34} + 3 q^{36} + 4 q^{38} + 4 q^{39} - 4 q^{42} + 4 q^{51} - 3 q^{53} + 4 q^{57} - 3 q^{63} + 3 q^{64} - q^{81} + 4 q^{82} - 3 q^{83} + q^{89} + q^{92} + 4 q^{96} - 3 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(643))\)

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
643.1.b \(\chi_{643}(642, \cdot)\) 643.1.b.a 1 1
643.1.b.b 2
643.1.d \(\chi_{643}(178, \cdot)\) None 0 2
643.1.f \(\chi_{643}(2, \cdot)\) None 0 106
643.1.h \(\chi_{643}(11, \cdot)\) None 0 212