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Properties

Label 256.5
Level 256
Weight 5
Dimension 4556
Nonzero newspaces 6
Sturm bound 20480
Trace bound 9

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Defining parameters

Level: \( N \) = \( 256 = 2^{8} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(20480\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(256))\).

Total New Old
Modular forms 8368 4660 3708
Cusp forms 8016 4556 3460
Eisenstein series 352 104 248

Trace form

\( 4556 q - 32 q^{2} - 24 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 24 q^{7} - 32 q^{8} - 40 q^{9} + O(q^{10}) \) \( 4556 q - 32 q^{2} - 24 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 24 q^{7} - 32 q^{8} - 40 q^{9} - 32 q^{10} - 24 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 24 q^{15} - 32 q^{16} - 48 q^{17} - 32 q^{18} - 24 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 24 q^{23} - 32 q^{24} - 40 q^{25} - 32 q^{26} - 24 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 16 q^{31} - 32 q^{32} - 56 q^{33} - 32 q^{34} - 24 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 24 q^{39} - 32 q^{40} - 40 q^{41} - 32 q^{42} - 24 q^{43} - 32 q^{44} + 616 q^{45} - 32 q^{46} - 24 q^{47} - 32 q^{48} + 9556 q^{49} - 32 q^{50} + 16104 q^{51} - 32 q^{52} - 1952 q^{53} - 32 q^{54} - 23576 q^{55} - 32 q^{56} - 29992 q^{57} - 32 q^{58} - 26136 q^{59} - 32 q^{60} - 15136 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} + 16056 q^{65} - 32 q^{66} + 37736 q^{67} - 32 q^{68} + 39136 q^{69} - 32 q^{70} + 39912 q^{71} - 32 q^{72} + 29400 q^{73} - 32 q^{74} + 4584 q^{75} - 32 q^{76} - 18848 q^{77} - 32 q^{78} - 50200 q^{79} - 32 q^{80} - 26292 q^{81} - 32 q^{82} - 24 q^{83} - 32 q^{84} - 5032 q^{85} - 32 q^{86} - 24 q^{87} - 32 q^{88} - 40 q^{89} - 32 q^{90} - 24 q^{91} - 32 q^{92} - 1328 q^{93} - 32 q^{94} - 16 q^{95} - 32 q^{96} - 56 q^{97} - 32 q^{98} - 672 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(256))\)

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
256.5.c \(\chi_{256}(255, \cdot)\) 256.5.c.a 1 1
256.5.c.b 1
256.5.c.c 2
256.5.c.d 2
256.5.c.e 2
256.5.c.f 2
256.5.c.g 4
256.5.c.h 4
256.5.c.i 4
256.5.c.j 4
256.5.c.k 4
256.5.d \(\chi_{256}(127, \cdot)\) 256.5.d.a 2 1
256.5.d.b 2
256.5.d.c 2
256.5.d.d 2
256.5.d.e 2
256.5.d.f 4
256.5.d.g 8
256.5.d.h 8
256.5.f \(\chi_{256}(63, \cdot)\) 256.5.f.a 8 2
256.5.f.b 8
256.5.f.c 24
256.5.f.d 24
256.5.h \(\chi_{256}(31, \cdot)\) n/a 120 4
256.5.j \(\chi_{256}(15, \cdot)\) n/a 248 8
256.5.l \(\chi_{256}(7, \cdot)\) None 0 16
256.5.n \(\chi_{256}(3, \cdot)\) n/a 4064 32

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(256))\) into lower level spaces

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