↑

Properties

Label 563.1
Level 563
Weight 1
Dimension 6
Nonzero newspaces 1
Newform subspaces 3
Sturm bound 26414
Trace bound 0

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 563 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 3 \)
Sturm bound: \(26414\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(563))\).

Total New Old
Modular forms 287 287 0
Cusp forms 6 6 0
Eisenstein series 281 281 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 2 0

Trace form

\( 6 q - 3 q^{3} + 2 q^{4} + q^{7} + 3 q^{9} + O(q^{10}) \) \( 6 q - 3 q^{3} + 2 q^{4} + q^{7} + 3 q^{9} - 4 q^{10} - q^{11} + q^{12} - q^{13} + 2 q^{16} - 3 q^{17} + q^{19} - 4 q^{21} - 3 q^{23} + 2 q^{25} - 3 q^{28} + 4 q^{30} - 2 q^{33} + 3 q^{36} - 2 q^{39} - q^{44} + q^{47} + q^{48} + 3 q^{49} - q^{52} - 4 q^{57} + q^{59} + q^{61} + 4 q^{62} - 3 q^{63} + 6 q^{64} + q^{67} + q^{68} - 4 q^{70} + q^{71} + q^{75} - 3 q^{76} - 2 q^{77} - 4 q^{86} - 2 q^{91} + q^{92} - 3 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(563))\)

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
563.1.b \(\chi_{563}(562, \cdot)\) 563.1.b.a 1 1
563.1.b.b 2
563.1.b.c 3
563.1.d \(\chi_{563}(2, \cdot)\) None 0 280