Properties

Label 1280.3
Level 1280
Weight 3
Dimension 50376
Nonzero newspaces 22
Sturm bound 294912
Trace bound 50

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 22 \)
Sturm bound: \(294912\)
Trace bound: \(50\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1280))\).

Total New Old
Modular forms 99712 51000 48712
Cusp forms 96896 50376 46520
Eisenstein series 2816 624 2192

Trace form

\( 50376 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 96 q^{5} - 192 q^{6} - 48 q^{7} - 64 q^{8} - 80 q^{9} + O(q^{10}) \) \( 50376 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 96 q^{5} - 192 q^{6} - 48 q^{7} - 64 q^{8} - 80 q^{9} - 96 q^{10} - 144 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 72 q^{15} - 192 q^{16} - 96 q^{17} - 64 q^{18} - 48 q^{19} - 96 q^{20} - 192 q^{21} - 64 q^{22} - 48 q^{23} - 64 q^{24} - 120 q^{25} - 192 q^{26} - 48 q^{27} - 64 q^{28} - 64 q^{29} - 96 q^{30} - 160 q^{31} - 64 q^{32} - 112 q^{33} - 64 q^{34} - 72 q^{35} - 192 q^{36} - 64 q^{37} - 64 q^{38} - 48 q^{39} - 96 q^{40} - 240 q^{41} - 64 q^{42} - 48 q^{43} - 64 q^{44} - 168 q^{45} - 192 q^{46} - 48 q^{47} - 64 q^{48} - 488 q^{49} - 96 q^{50} - 912 q^{51} - 64 q^{52} - 704 q^{53} - 64 q^{54} - 584 q^{55} - 192 q^{56} - 848 q^{57} - 64 q^{58} - 560 q^{59} - 96 q^{60} - 448 q^{61} - 64 q^{62} - 32 q^{63} - 64 q^{64} - 88 q^{65} - 192 q^{66} + 592 q^{67} - 64 q^{68} + 704 q^{69} - 96 q^{70} + 880 q^{71} - 64 q^{72} + 1200 q^{73} - 64 q^{74} + 696 q^{75} - 192 q^{76} + 832 q^{77} - 64 q^{78} + 976 q^{79} - 96 q^{80} + 360 q^{81} - 64 q^{82} - 48 q^{83} - 64 q^{84} + 104 q^{85} - 192 q^{86} - 48 q^{87} - 64 q^{88} - 80 q^{89} - 96 q^{90} - 144 q^{91} - 64 q^{92} + 224 q^{93} - 64 q^{94} - 80 q^{95} - 192 q^{96} - 112 q^{97} - 64 q^{98} + 96 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1280))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1280.3.b \(\chi_{1280}(511, \cdot)\) 1280.3.b.a 4 1
1280.3.b.b 4
1280.3.b.c 4
1280.3.b.d 4
1280.3.b.e 8
1280.3.b.f 8
1280.3.b.g 8
1280.3.b.h 8
1280.3.b.i 16
1280.3.e \(\chi_{1280}(639, \cdot)\) 1280.3.e.a 2 1
1280.3.e.b 2
1280.3.e.c 2
1280.3.e.d 2
1280.3.e.e 4
1280.3.e.f 6
1280.3.e.g 6
1280.3.e.h 6
1280.3.e.i 6
1280.3.e.j 8
1280.3.e.k 24
1280.3.e.l 24
1280.3.g \(\chi_{1280}(1151, \cdot)\) 1280.3.g.a 4 1
1280.3.g.b 4
1280.3.g.c 4
1280.3.g.d 4
1280.3.g.e 8
1280.3.g.f 8
1280.3.g.g 16
1280.3.g.h 16
1280.3.h \(\chi_{1280}(1279, \cdot)\) 1280.3.h.a 2 1
1280.3.h.b 2
1280.3.h.c 2
1280.3.h.d 2
1280.3.h.e 4
1280.3.h.f 4
1280.3.h.g 4
1280.3.h.h 8
1280.3.h.i 8
1280.3.h.j 8
1280.3.h.k 8
1280.3.h.l 8
1280.3.h.m 16
1280.3.h.n 16
1280.3.i \(\chi_{1280}(833, \cdot)\) n/a 192 2
1280.3.k \(\chi_{1280}(319, \cdot)\) n/a 192 2
1280.3.m \(\chi_{1280}(897, \cdot)\) n/a 184 2
1280.3.p \(\chi_{1280}(257, \cdot)\) n/a 184 2
1280.3.r \(\chi_{1280}(191, \cdot)\) n/a 128 2
1280.3.t \(\chi_{1280}(193, \cdot)\) n/a 192 2
1280.3.v \(\chi_{1280}(33, \cdot)\) n/a 368 4
1280.3.w \(\chi_{1280}(31, \cdot)\) n/a 256 4
1280.3.y \(\chi_{1280}(159, \cdot)\) n/a 368 4
1280.3.bb \(\chi_{1280}(353, \cdot)\) n/a 368 4
1280.3.bc \(\chi_{1280}(17, \cdot)\) n/a 752 8
1280.3.bg \(\chi_{1280}(111, \cdot)\) n/a 512 8
1280.3.bh \(\chi_{1280}(79, \cdot)\) n/a 752 8
1280.3.bi \(\chi_{1280}(177, \cdot)\) n/a 752 8
1280.3.bk \(\chi_{1280}(57, \cdot)\) None 0 16
1280.3.bn \(\chi_{1280}(39, \cdot)\) None 0 16
1280.3.bp \(\chi_{1280}(71, \cdot)\) None 0 16
1280.3.bq \(\chi_{1280}(137, \cdot)\) None 0 16
1280.3.bs \(\chi_{1280}(53, \cdot)\) n/a 12224 32
1280.3.bu \(\chi_{1280}(19, \cdot)\) n/a 12224 32
1280.3.bx \(\chi_{1280}(11, \cdot)\) n/a 8192 32
1280.3.bz \(\chi_{1280}(13, \cdot)\) n/a 12224 32

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1280))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1280)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(640))\)\(^{\oplus 2}\)