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Properties

Label 1056.2
Level 1056
Weight 2
Dimension 12564
Nonzero newspaces 24
Sturm bound 122880
Trace bound 13

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Defining parameters

Level: \( N \) = \( 1056 = 2^{5} \cdot 3 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(122880\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1056))\).

Total New Old
Modular forms 32000 12924 19076
Cusp forms 29441 12564 16877
Eisenstein series 2559 360 2199

Trace form

\( 12564 q - 26 q^{3} - 64 q^{4} - 8 q^{5} - 32 q^{6} - 52 q^{7} - 56 q^{9} + O(q^{10}) \) \( 12564 q - 26 q^{3} - 64 q^{4} - 8 q^{5} - 32 q^{6} - 52 q^{7} - 56 q^{9} - 32 q^{10} - 40 q^{12} - 40 q^{13} + 64 q^{14} - 6 q^{15} + 16 q^{16} + 32 q^{17} - 16 q^{18} - 36 q^{19} + 64 q^{20} - 48 q^{22} + 48 q^{23} - 56 q^{24} - 60 q^{25} - 80 q^{26} + 46 q^{27} - 144 q^{28} - 8 q^{29} - 128 q^{30} + 44 q^{31} - 80 q^{32} - 92 q^{33} - 192 q^{34} + 96 q^{35} - 136 q^{36} - 104 q^{37} - 80 q^{38} + 10 q^{39} - 144 q^{40} - 16 q^{41} - 152 q^{42} - 32 q^{43} - 8 q^{44} - 144 q^{45} - 64 q^{46} - 48 q^{47} - 136 q^{48} - 116 q^{49} - 48 q^{50} - 62 q^{51} - 160 q^{52} + 24 q^{53} - 136 q^{54} - 116 q^{55} - 112 q^{56} - 92 q^{57} - 208 q^{58} - 128 q^{59} - 152 q^{60} + 56 q^{61} - 96 q^{62} - 54 q^{63} - 208 q^{64} - 16 q^{65} - 60 q^{66} - 208 q^{67} + 16 q^{68} + 96 q^{69} - 112 q^{70} - 40 q^{71} + 88 q^{72} + 144 q^{73} + 64 q^{74} - 26 q^{75} - 64 q^{76} + 224 q^{77} + 56 q^{78} + 148 q^{79} + 112 q^{80} + 56 q^{81} + 96 q^{82} + 200 q^{83} + 232 q^{84} + 384 q^{85} + 128 q^{86} - 48 q^{87} + 16 q^{88} + 160 q^{89} + 232 q^{90} + 196 q^{91} + 160 q^{92} + 104 q^{93} + 112 q^{94} + 168 q^{95} + 248 q^{96} + 96 q^{97} + 160 q^{98} - 66 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1056))\)

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
1056.2.a \(\chi_{1056}(1, \cdot)\) 1056.2.a.a 1 1
1056.2.a.b 1
1056.2.a.c 1
1056.2.a.d 1
1056.2.a.e 1
1056.2.a.f 1
1056.2.a.g 1
1056.2.a.h 1
1056.2.a.i 1
1056.2.a.j 1
1056.2.a.k 2
1056.2.a.l 2
1056.2.a.m 3
1056.2.a.n 3
1056.2.b \(\chi_{1056}(65, \cdot)\) 1056.2.b.a 2 1
1056.2.b.b 2
1056.2.b.c 2
1056.2.b.d 2
1056.2.b.e 4
1056.2.b.f 4
1056.2.b.g 8
1056.2.b.h 8
1056.2.b.i 8
1056.2.b.j 8
1056.2.d \(\chi_{1056}(287, \cdot)\) 1056.2.d.a 20 1
1056.2.d.b 20
1056.2.f \(\chi_{1056}(529, \cdot)\) 1056.2.f.a 2 1
1056.2.f.b 2
1056.2.f.c 2
1056.2.f.d 4
1056.2.f.e 4
1056.2.f.f 6
1056.2.h \(\chi_{1056}(175, \cdot)\) 1056.2.h.a 2 1
1056.2.h.b 2
1056.2.h.c 4
1056.2.h.d 4
1056.2.h.e 12
1056.2.k \(\chi_{1056}(815, \cdot)\) 1056.2.k.a 8 1
1056.2.k.b 32
1056.2.m \(\chi_{1056}(593, \cdot)\) 1056.2.m.a 4 1
1056.2.m.b 40
1056.2.o \(\chi_{1056}(703, \cdot)\) 1056.2.o.a 4 1
1056.2.o.b 4
1056.2.o.c 4
1056.2.o.d 12
1056.2.q \(\chi_{1056}(439, \cdot)\) None 0 2
1056.2.t \(\chi_{1056}(265, \cdot)\) None 0 2
1056.2.u \(\chi_{1056}(23, \cdot)\) None 0 2
1056.2.x \(\chi_{1056}(329, \cdot)\) None 0 2
1056.2.y \(\chi_{1056}(97, \cdot)\) 1056.2.y.a 4 4
1056.2.y.b 4
1056.2.y.c 8
1056.2.y.d 8
1056.2.y.e 12
1056.2.y.f 12
1056.2.y.g 12
1056.2.y.h 12
1056.2.y.i 12
1056.2.y.j 12
1056.2.bb \(\chi_{1056}(133, \cdot)\) n/a 320 4
1056.2.bc \(\chi_{1056}(197, \cdot)\) n/a 752 4
1056.2.bd \(\chi_{1056}(155, \cdot)\) n/a 640 4
1056.2.be \(\chi_{1056}(43, \cdot)\) n/a 384 4
1056.2.bi \(\chi_{1056}(127, \cdot)\) 1056.2.bi.a 16 4
1056.2.bi.b 32
1056.2.bi.c 48
1056.2.bk \(\chi_{1056}(17, \cdot)\) n/a 176 4
1056.2.bm \(\chi_{1056}(47, \cdot)\) n/a 176 4
1056.2.bp \(\chi_{1056}(79, \cdot)\) 1056.2.bp.a 48 4
1056.2.bp.b 48
1056.2.br \(\chi_{1056}(49, \cdot)\) 1056.2.br.a 96 4
1056.2.bt \(\chi_{1056}(191, \cdot)\) n/a 192 4
1056.2.bv \(\chi_{1056}(161, \cdot)\) n/a 192 4
1056.2.bw \(\chi_{1056}(41, \cdot)\) None 0 8
1056.2.bz \(\chi_{1056}(71, \cdot)\) None 0 8
1056.2.ca \(\chi_{1056}(25, \cdot)\) None 0 8
1056.2.cd \(\chi_{1056}(7, \cdot)\) None 0 8
1056.2.cg \(\chi_{1056}(19, \cdot)\) n/a 1536 16
1056.2.ch \(\chi_{1056}(59, \cdot)\) n/a 3008 16
1056.2.ci \(\chi_{1056}(29, \cdot)\) n/a 3008 16
1056.2.cj \(\chi_{1056}(37, \cdot)\) n/a 1536 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1056))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1056)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 2}\)