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Properties

Label 256.4
Level 256
Weight 4
Dimension 3404
Nonzero newspaces 6
Sturm bound 16384
Trace bound 9

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Defining parameters

Level: \( N \) = \( 256 = 2^{8} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(16384\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(256))\).

Total New Old
Modular forms 6320 3508 2812
Cusp forms 5968 3404 2564
Eisenstein series 352 104 248

Trace form

\( 3404 q - 32 q^{2} - 24 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 24 q^{7} - 32 q^{8} - 40 q^{9} + O(q^{10}) \) \( 3404 q - 32 q^{2} - 24 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 24 q^{7} - 32 q^{8} - 40 q^{9} - 32 q^{10} - 24 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 24 q^{15} - 32 q^{16} - 48 q^{17} - 32 q^{18} - 24 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 24 q^{23} - 32 q^{24} - 40 q^{25} - 32 q^{26} - 24 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 56 q^{33} - 32 q^{34} - 24 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 24 q^{39} - 32 q^{40} - 40 q^{41} - 32 q^{42} - 24 q^{43} - 32 q^{44} - 248 q^{45} - 32 q^{46} - 24 q^{47} - 32 q^{48} - 1420 q^{49} - 32 q^{50} - 3000 q^{51} - 32 q^{52} - 1536 q^{53} - 32 q^{54} - 600 q^{55} - 32 q^{56} + 1304 q^{57} - 32 q^{58} + 2728 q^{59} - 32 q^{60} + 3616 q^{61} - 32 q^{62} + 5024 q^{63} - 32 q^{64} + 3832 q^{65} - 32 q^{66} + 4056 q^{67} - 32 q^{68} + 2080 q^{69} - 32 q^{70} + 424 q^{71} - 32 q^{72} - 1768 q^{73} - 32 q^{74} - 4440 q^{75} - 32 q^{76} - 3840 q^{77} - 32 q^{78} - 5688 q^{79} - 32 q^{80} - 2964 q^{81} - 32 q^{82} - 24 q^{83} - 32 q^{84} - 1032 q^{85} - 32 q^{86} - 24 q^{87} - 32 q^{88} - 40 q^{89} - 32 q^{90} - 24 q^{91} - 32 q^{92} + 400 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 56 q^{97} - 32 q^{98} - 240 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(256))\)

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
256.4.a \(\chi_{256}(1, \cdot)\) 256.4.a.a 1 1
256.4.a.b 1
256.4.a.c 1
256.4.a.d 1
256.4.a.e 1
256.4.a.f 1
256.4.a.g 1
256.4.a.h 1
256.4.a.i 2
256.4.a.j 2
256.4.a.k 2
256.4.a.l 2
256.4.a.m 2
256.4.a.n 4
256.4.b \(\chi_{256}(129, \cdot)\) 256.4.b.a 2 1
256.4.b.b 2
256.4.b.c 2
256.4.b.d 2
256.4.b.e 2
256.4.b.f 2
256.4.b.g 2
256.4.b.h 4
256.4.b.i 4
256.4.e \(\chi_{256}(65, \cdot)\) 256.4.e.a 8 2
256.4.e.b 8
256.4.e.c 16
256.4.e.d 16
256.4.g \(\chi_{256}(33, \cdot)\) 256.4.g.a 44 4
256.4.g.b 44
256.4.i \(\chi_{256}(17, \cdot)\) n/a 184 8
256.4.k \(\chi_{256}(9, \cdot)\) None 0 16
256.4.m \(\chi_{256}(5, \cdot)\) n/a 3040 32

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(256))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(256)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 1}\)