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Properties

Label 256.7
Level 256
Weight 7
Dimension 6860
Nonzero newspaces 6
Sturm bound 28672
Trace bound 9

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Defining parameters

Level: \( N \) = \( 256 = 2^{8} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(28672\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(256))\).

Total New Old
Modular forms 12464 6964 5500
Cusp forms 12112 6860 5252
Eisenstein series 352 104 248

Trace form

\( 6860 q - 32 q^{2} - 24 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 24 q^{7} - 32 q^{8} - 40 q^{9} + O(q^{10}) \) \( 6860 q - 32 q^{2} - 24 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 24 q^{7} - 32 q^{8} - 40 q^{9} - 32 q^{10} - 24 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 24 q^{15} - 32 q^{16} - 48 q^{17} - 32 q^{18} - 24 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 24 q^{23} - 32 q^{24} - 40 q^{25} - 32 q^{26} - 24 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 16 q^{31} - 32 q^{32} - 56 q^{33} - 32 q^{34} - 24 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 24 q^{39} - 32 q^{40} - 40 q^{41} - 32 q^{42} - 24 q^{43} - 32 q^{44} + 5800 q^{45} - 32 q^{46} - 24 q^{47} - 32 q^{48} + 470548 q^{49} - 32 q^{50} - 321432 q^{51} - 32 q^{52} - 887392 q^{53} - 32 q^{54} - 465432 q^{55} - 32 q^{56} + 1088600 q^{57} - 32 q^{58} + 1772264 q^{59} - 32 q^{60} + 1305952 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 1491400 q^{65} - 32 q^{66} - 3019224 q^{67} - 32 q^{68} - 2166944 q^{69} - 32 q^{70} - 534040 q^{71} - 32 q^{72} + 2056280 q^{73} - 32 q^{74} + 4292328 q^{75} - 32 q^{76} + 1865888 q^{77} - 32 q^{78} - 1721880 q^{79} - 32 q^{80} - 2125812 q^{81} - 32 q^{82} - 24 q^{83} - 32 q^{84} - 125032 q^{85} - 32 q^{86} - 24 q^{87} - 32 q^{88} - 40 q^{89} - 32 q^{90} - 24 q^{91} - 32 q^{92} - 11696 q^{93} - 32 q^{94} - 16 q^{95} - 32 q^{96} - 56 q^{97} - 32 q^{98} - 5856 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(256))\)

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
256.7.c \(\chi_{256}(255, \cdot)\) 256.7.c.a 1 1
256.7.c.b 1
256.7.c.c 2
256.7.c.d 2
256.7.c.e 2
256.7.c.f 2
256.7.c.g 4
256.7.c.h 4
256.7.c.i 6
256.7.c.j 6
256.7.c.k 8
256.7.c.l 8
256.7.d \(\chi_{256}(127, \cdot)\) 256.7.d.a 2 1
256.7.d.b 2
256.7.d.c 2
256.7.d.d 4
256.7.d.e 4
256.7.d.f 4
256.7.d.g 4
256.7.d.h 12
256.7.d.i 12
256.7.f \(\chi_{256}(63, \cdot)\) 256.7.f.a 16 2
256.7.f.b 16
256.7.f.c 32
256.7.f.d 32
256.7.h \(\chi_{256}(31, \cdot)\) n/a 184 4
256.7.j \(\chi_{256}(15, \cdot)\) n/a 376 8
256.7.l \(\chi_{256}(7, \cdot)\) None 0 16
256.7.n \(\chi_{256}(3, \cdot)\) n/a 6112 32

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(256))\) into lower level spaces

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