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Properties

Label 640.3
Level 640
Weight 3
Dimension 12528
Nonzero newspaces 18
Sturm bound 73728
Trace bound 33

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Defining parameters

Level: \( N \) = \( 640 = 2^{7} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(73728\)
Trace bound: \(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(640))\).

Total New Old
Modular forms 25216 12816 12400
Cusp forms 23936 12528 11408
Eisenstein series 1280 288 992

Trace form

\( 12528 q - 32 q^{2} - 24 q^{3} - 32 q^{4} - 48 q^{5} - 96 q^{6} - 24 q^{7} - 32 q^{8} - 40 q^{9} + O(q^{10}) \) \( 12528 q - 32 q^{2} - 24 q^{3} - 32 q^{4} - 48 q^{5} - 96 q^{6} - 24 q^{7} - 32 q^{8} - 40 q^{9} - 48 q^{10} - 72 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 40 q^{15} - 96 q^{16} - 48 q^{17} - 32 q^{18} - 24 q^{19} - 48 q^{20} - 168 q^{21} - 32 q^{22} - 152 q^{23} - 32 q^{24} - 156 q^{25} - 96 q^{26} - 216 q^{27} - 32 q^{28} - 96 q^{29} - 48 q^{30} - 64 q^{31} - 32 q^{32} + 64 q^{33} - 32 q^{34} + 60 q^{35} - 96 q^{36} + 160 q^{37} - 32 q^{38} + 360 q^{39} - 48 q^{40} + 200 q^{41} - 32 q^{42} + 168 q^{43} - 32 q^{44} + 124 q^{45} - 96 q^{46} - 32 q^{47} - 32 q^{48} + 344 q^{49} + 576 q^{50} + 384 q^{51} + 2080 q^{52} + 608 q^{53} + 2272 q^{54} + 220 q^{55} + 1472 q^{56} + 728 q^{57} + 1408 q^{58} + 232 q^{59} + 528 q^{60} + 160 q^{61} + 160 q^{62} + 16 q^{63} - 416 q^{64} - 176 q^{65} - 1248 q^{66} - 344 q^{67} - 992 q^{68} - 872 q^{69} - 1392 q^{70} - 584 q^{71} - 2624 q^{72} - 1320 q^{73} - 2496 q^{74} - 420 q^{75} - 3424 q^{76} - 1320 q^{77} - 2912 q^{78} - 1040 q^{79} - 864 q^{80} - 1688 q^{81} - 32 q^{82} - 984 q^{83} - 32 q^{84} - 568 q^{85} - 96 q^{86} - 920 q^{87} - 32 q^{88} - 808 q^{89} - 48 q^{90} - 456 q^{91} - 32 q^{92} - 224 q^{93} - 32 q^{94} - 32 q^{95} - 96 q^{96} + 192 q^{97} - 32 q^{98} + 416 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(640))\)

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
640.3.b \(\chi_{640}(511, \cdot)\) 640.3.b.a 16 1
640.3.b.b 16
640.3.e \(\chi_{640}(319, \cdot)\) 640.3.e.a 2 1
640.3.e.b 2
640.3.e.c 2
640.3.e.d 2
640.3.e.e 4
640.3.e.f 4
640.3.e.g 8
640.3.e.h 8
640.3.e.i 16
640.3.g \(\chi_{640}(191, \cdot)\) 640.3.g.a 4 1
640.3.g.b 4
640.3.g.c 8
640.3.g.d 16
640.3.h \(\chi_{640}(639, \cdot)\) 640.3.h.a 24 1
640.3.h.b 24
640.3.i \(\chi_{640}(33, \cdot)\) 640.3.i.a 44 2
640.3.i.b 44
640.3.k \(\chi_{640}(159, \cdot)\) 640.3.k.a 44 2
640.3.k.b 44
640.3.m \(\chi_{640}(193, \cdot)\) 640.3.m.a 2 2
640.3.m.b 2
640.3.m.c 2
640.3.m.d 2
640.3.m.e 2
640.3.m.f 2
640.3.m.g 2
640.3.m.h 2
640.3.m.i 4
640.3.m.j 4
640.3.m.k 12
640.3.m.l 12
640.3.m.m 12
640.3.m.n 12
640.3.m.o 24
640.3.p \(\chi_{640}(257, \cdot)\) 640.3.p.a 12 2
640.3.p.b 12
640.3.p.c 12
640.3.p.d 12
640.3.p.e 12
640.3.p.f 12
640.3.p.g 12
640.3.p.h 12
640.3.r \(\chi_{640}(31, \cdot)\) 640.3.r.a 32 2
640.3.r.b 32
640.3.t \(\chi_{640}(353, \cdot)\) 640.3.t.a 44 2
640.3.t.b 44
640.3.v \(\chi_{640}(177, \cdot)\) n/a 184 4
640.3.w \(\chi_{640}(111, \cdot)\) n/a 128 4
640.3.y \(\chi_{640}(79, \cdot)\) n/a 184 4
640.3.bb \(\chi_{640}(17, \cdot)\) n/a 184 4
640.3.bc \(\chi_{640}(137, \cdot)\) None 0 8
640.3.bg \(\chi_{640}(71, \cdot)\) None 0 8
640.3.bh \(\chi_{640}(39, \cdot)\) None 0 8
640.3.bi \(\chi_{640}(57, \cdot)\) None 0 8
640.3.bk \(\chi_{640}(13, \cdot)\) n/a 3040 16
640.3.bn \(\chi_{640}(19, \cdot)\) n/a 3040 16
640.3.bp \(\chi_{640}(11, \cdot)\) n/a 2048 16
640.3.bq \(\chi_{640}(53, \cdot)\) n/a 3040 16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(640))\) into lower level spaces

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