Properties

Label 571.1
Level 571
Weight 1
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 27170
Trace bound 0

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Defining parameters

Level: \( N \) = \( 571 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(27170\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(571))\).

Total New Old
Modular forms 287 287 0
Cusp forms 2 2 0
Eisenstein series 285 285 0

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

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

Trace form

\( 2 q + 2 q^{4} - q^{5} + 2 q^{9} + O(q^{10}) \) \( 2 q + 2 q^{4} - q^{5} + 2 q^{9} - q^{11} - q^{13} + 2 q^{16} - q^{20} - q^{23} + q^{25} - q^{29} - q^{31} + 2 q^{36} - q^{37} - q^{43} - q^{44} - q^{45} + 2 q^{49} - q^{52} - 2 q^{55} - q^{59} - q^{61} + 2 q^{64} - 2 q^{65} - q^{80} + 2 q^{81} - q^{83} - q^{92} - q^{97} - q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(571))\)

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
571.1.b \(\chi_{571}(570, \cdot)\) 571.1.b.a 2 1
571.1.e \(\chi_{571}(110, \cdot)\) None 0 2
571.1.f \(\chi_{571}(90, \cdot)\) None 0 4
571.1.i \(\chi_{571}(69, \cdot)\) None 0 8
571.1.j \(\chi_{571}(8, \cdot)\) None 0 18
571.1.m \(\chi_{571}(2, \cdot)\) None 0 36
571.1.n \(\chi_{571}(7, \cdot)\) None 0 72
571.1.p \(\chi_{571}(3, \cdot)\) None 0 144