↑

Properties

Label 251.1
Level 251
Weight 1
Dimension 3
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 5250
Trace bound 0

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 251 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(5250\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(251))\).

Total New Old
Modular forms 128 128 0
Cusp forms 3 3 0
Eisenstein series 125 125 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3 q - q^{3} + 3 q^{4} - q^{5} - q^{7} + 2 q^{9} + O(q^{10}) \) \( 3 q - q^{3} + 3 q^{4} - q^{5} - q^{7} + 2 q^{9} - q^{12} - q^{13} - 2 q^{15} + 3 q^{16} - q^{17} - q^{20} - 2 q^{21} - q^{23} + 2 q^{25} - 2 q^{27} - q^{28} - q^{31} - 2 q^{35} + 2 q^{36} - 2 q^{39} - q^{41} - 3 q^{45} - q^{48} + 2 q^{49} - 2 q^{51} - q^{52} - 2 q^{60} + 4 q^{63} + 3 q^{64} + 5 q^{65} - q^{67} - q^{68} + 5 q^{69} - q^{73} + 4 q^{75} - q^{79} - q^{80} + q^{81} + 6 q^{83} - 2 q^{84} - 2 q^{85} - q^{89} - 2 q^{91} - q^{92} + 5 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(251))\)

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
251.1.b \(\chi_{251}(250, \cdot)\) 251.1.b.a 3 1
251.1.d \(\chi_{251}(32, \cdot)\) None 0 4
251.1.f \(\chi_{251}(2, \cdot)\) None 0 20
251.1.h \(\chi_{251}(6, \cdot)\) None 0 100