↑

Properties

Label 257.6
Level 257
Weight 6
Dimension 13632
Nonzero newspaces 8
Sturm bound 33024
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 257 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(33024\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(257))\).

Total New Old
Modular forms 13888 13886 2
Cusp forms 13632 13632 0
Eisenstein series 256 254 2

Trace form

\( 13632 q - 128 q^{2} - 128 q^{3} - 128 q^{4} - 128 q^{5} - 128 q^{6} - 128 q^{7} - 128 q^{8} - 128 q^{9} + O(q^{10}) \) \( 13632 q - 128 q^{2} - 128 q^{3} - 128 q^{4} - 128 q^{5} - 128 q^{6} - 128 q^{7} - 128 q^{8} - 128 q^{9} - 128 q^{10} - 128 q^{11} - 128 q^{12} - 128 q^{13} - 128 q^{14} - 128 q^{15} - 128 q^{16} - 128 q^{17} - 128 q^{18} - 128 q^{19} - 128 q^{20} - 128 q^{21} - 128 q^{22} - 128 q^{23} - 128 q^{24} - 128 q^{25} - 128 q^{26} - 128 q^{27} - 128 q^{28} - 128 q^{29} - 128 q^{30} - 128 q^{31} - 128 q^{32} - 128 q^{33} - 128 q^{34} - 128 q^{35} - 128 q^{36} - 128 q^{37} - 128 q^{38} - 128 q^{39} - 128 q^{40} - 128 q^{41} - 128 q^{42} - 128 q^{43} - 128 q^{44} - 128 q^{45} - 128 q^{46} - 128 q^{47} - 128 q^{48} - 128 q^{49} - 128 q^{50} - 128 q^{51} - 128 q^{52} - 128 q^{53} - 128 q^{54} - 128 q^{55} - 128 q^{56} - 128 q^{57} - 128 q^{58} - 128 q^{59} - 128 q^{60} - 128 q^{61} - 128 q^{62} - 128 q^{63} - 128 q^{64} - 128 q^{65} - 128 q^{66} - 128 q^{67} - 128 q^{68} - 128 q^{69} - 128 q^{70} - 128 q^{71} - 128 q^{72} - 128 q^{73} - 128 q^{74} - 128 q^{75} - 128 q^{76} - 128 q^{77} - 128 q^{78} - 128 q^{79} - 128 q^{80} - 128 q^{81} - 128 q^{82} - 128 q^{83} - 128 q^{84} - 128 q^{85} - 128 q^{86} - 128 q^{87} - 128 q^{88} - 128 q^{89} - 128 q^{90} - 128 q^{91} - 128 q^{92} - 128 q^{93} - 128 q^{94} - 128 q^{95} - 128 q^{96} - 128 q^{97} - 128 q^{98} - 128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(257))\)

We only show spaces with even 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
257.6.a \(\chi_{257}(1, \cdot)\) 257.6.a.a 49 1
257.6.a.b 57
257.6.b \(\chi_{257}(256, \cdot)\) n/a 106 1
257.6.c \(\chi_{257}(16, \cdot)\) n/a 212 2
257.6.d \(\chi_{257}(4, \cdot)\) n/a 424 4
257.6.e \(\chi_{257}(2, \cdot)\) n/a 848 8
257.6.f \(\chi_{257}(15, \cdot)\) n/a 1696 16
257.6.g \(\chi_{257}(11, \cdot)\) n/a 3392 32
257.6.h \(\chi_{257}(9, \cdot)\) n/a 6848 64

"n/a" means that newforms for that character have not been added to the database yet