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Properties

Label 2256.2
Level 2256
Weight 2
Dimension 59156
Nonzero newspaces 16
Sturm bound 565248
Trace bound 9

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Defining parameters

Level: \( N \) = \( 2256 = 2^{4} \cdot 3 \cdot 47 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(565248\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2256))\).

Total New Old
Modular forms 143888 59968 83920
Cusp forms 138737 59156 79581
Eisenstein series 5151 812 4339

Trace form

\( 59156 q - 67 q^{3} - 168 q^{4} + 4 q^{5} - 76 q^{6} - 122 q^{7} + 24 q^{8} - 13 q^{9} + O(q^{10}) \) \( 59156 q - 67 q^{3} - 168 q^{4} + 4 q^{5} - 76 q^{6} - 122 q^{7} + 24 q^{8} - 13 q^{9} - 168 q^{10} + 24 q^{11} - 92 q^{12} - 210 q^{13} - 24 q^{14} - 49 q^{15} - 216 q^{16} - 4 q^{17} - 108 q^{18} - 106 q^{19} - 32 q^{20} - 123 q^{21} - 216 q^{22} - 16 q^{23} - 148 q^{24} - 64 q^{25} - 40 q^{26} - 91 q^{27} - 184 q^{28} + 20 q^{29} - 132 q^{30} - 170 q^{31} - 191 q^{33} - 168 q^{34} - 48 q^{35} - 124 q^{36} - 162 q^{37} + 16 q^{38} - 105 q^{39} - 136 q^{40} + 12 q^{41} - 4 q^{42} - 138 q^{43} + 80 q^{44} - 87 q^{45} - 88 q^{46} - 56 q^{48} - 324 q^{49} + 72 q^{50} - 137 q^{51} - 120 q^{52} - 28 q^{53} + 4 q^{54} - 202 q^{55} - 7 q^{57} - 216 q^{58} - 56 q^{59} - 108 q^{60} - 338 q^{61} + 24 q^{62} - 85 q^{63} - 312 q^{64} + 24 q^{65} - 196 q^{66} - 170 q^{67} - 64 q^{68} - 171 q^{69} - 328 q^{70} + 16 q^{71} - 164 q^{72} - 106 q^{73} - 104 q^{74} - 31 q^{75} - 312 q^{76} - 32 q^{77} - 188 q^{78} - 106 q^{79} - 16 q^{80} - 221 q^{81} - 232 q^{82} + 72 q^{83} - 76 q^{84} - 254 q^{85} + 32 q^{86} + 39 q^{87} - 120 q^{88} + 12 q^{89} - 44 q^{90} - 10 q^{91} + 32 q^{92} - 60 q^{93} - 144 q^{94} + 112 q^{95} + 20 q^{96} - 346 q^{97} + 80 q^{98} + 59 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2256))\)

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
2256.2.a \(\chi_{2256}(1, \cdot)\) 2256.2.a.a 1 1
2256.2.a.b 1
2256.2.a.c 1
2256.2.a.d 1
2256.2.a.e 1
2256.2.a.f 1
2256.2.a.g 1
2256.2.a.h 1
2256.2.a.i 1
2256.2.a.j 1
2256.2.a.k 1
2256.2.a.l 1
2256.2.a.m 1
2256.2.a.n 1
2256.2.a.o 1
2256.2.a.p 1
2256.2.a.q 2
2256.2.a.r 2
2256.2.a.s 2
2256.2.a.t 3
2256.2.a.u 3
2256.2.a.v 3
2256.2.a.w 3
2256.2.a.x 3
2256.2.a.y 4
2256.2.a.z 5
2256.2.c \(\chi_{2256}(751, \cdot)\) 2256.2.c.a 16 1
2256.2.c.b 32
2256.2.e \(\chi_{2256}(95, \cdot)\) 2256.2.e.a 2 1
2256.2.e.b 2
2256.2.e.c 16
2256.2.e.d 16
2256.2.e.e 28
2256.2.e.f 28
2256.2.g \(\chi_{2256}(1129, \cdot)\) None 0 1
2256.2.i \(\chi_{2256}(281, \cdot)\) None 0 1
2256.2.k \(\chi_{2256}(1223, \cdot)\) None 0 1
2256.2.m \(\chi_{2256}(1879, \cdot)\) None 0 1
2256.2.o \(\chi_{2256}(1409, \cdot)\) 2256.2.o.a 4 1
2256.2.o.b 10
2256.2.o.c 16
2256.2.o.d 16
2256.2.o.e 48
2256.2.q \(\chi_{2256}(845, \cdot)\) n/a 760 2
2256.2.s \(\chi_{2256}(565, \cdot)\) n/a 368 2
2256.2.u \(\chi_{2256}(659, \cdot)\) n/a 736 2
2256.2.w \(\chi_{2256}(187, \cdot)\) n/a 384 2
2256.2.y \(\chi_{2256}(49, \cdot)\) n/a 1056 22
2256.2.ba \(\chi_{2256}(113, \cdot)\) n/a 2068 22
2256.2.bc \(\chi_{2256}(151, \cdot)\) None 0 22
2256.2.be \(\chi_{2256}(71, \cdot)\) None 0 22
2256.2.bg \(\chi_{2256}(41, \cdot)\) None 0 22
2256.2.bi \(\chi_{2256}(25, \cdot)\) None 0 22
2256.2.bk \(\chi_{2256}(143, \cdot)\) n/a 2112 22
2256.2.bm \(\chi_{2256}(31, \cdot)\) n/a 1056 22
2256.2.bp \(\chi_{2256}(19, \cdot)\) n/a 8448 44
2256.2.br \(\chi_{2256}(59, \cdot)\) n/a 16720 44
2256.2.bt \(\chi_{2256}(37, \cdot)\) n/a 8448 44
2256.2.bv \(\chi_{2256}(5, \cdot)\) n/a 16720 44

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2256))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2256)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(94))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(141))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(188))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(282))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(376))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(564))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(752))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1128))\)\(^{\oplus 2}\)