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Properties

Label 640.4
Level 640
Weight 4
Dimension 18864
Nonzero newspaces 18
Sturm bound 98304
Trace bound 33

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Defining parameters

Level: \( N \) = \( 640 = 2^{7} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(98304\)
Trace bound: \(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(640))\).

Total New Old
Modular forms 37504 19152 18352
Cusp forms 36224 18864 17360
Eisenstein series 1280 288 992

Trace form

\( 18864 q - 32 q^{2} - 24 q^{3} - 32 q^{4} - 48 q^{5} - 96 q^{6} - 24 q^{7} - 32 q^{8} - 40 q^{9} + O(q^{10}) \) \( 18864 q - 32 q^{2} - 24 q^{3} - 32 q^{4} - 48 q^{5} - 96 q^{6} - 24 q^{7} - 32 q^{8} - 40 q^{9} - 48 q^{10} - 72 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 96 q^{16} - 48 q^{17} - 32 q^{18} - 24 q^{19} - 48 q^{20} + 120 q^{21} - 32 q^{22} + 632 q^{23} - 32 q^{24} + 116 q^{25} - 96 q^{26} - 552 q^{27} - 32 q^{28} - 832 q^{29} - 48 q^{30} - 1568 q^{31} - 32 q^{32} - 1920 q^{33} - 32 q^{34} - 492 q^{35} - 96 q^{36} - 64 q^{37} - 32 q^{38} + 1176 q^{39} - 48 q^{40} + 1768 q^{41} - 32 q^{42} + 1592 q^{43} - 32 q^{44} + 236 q^{45} - 96 q^{46} - 16 q^{47} - 32 q^{48} - 2792 q^{49} - 5760 q^{50} - 2832 q^{51} - 13280 q^{52} - 3040 q^{53} - 6944 q^{54} - 324 q^{55} + 1472 q^{56} + 2648 q^{57} + 9472 q^{58} + 2728 q^{59} + 9744 q^{60} + 7200 q^{61} + 11680 q^{62} + 4976 q^{63} + 24160 q^{64} + 3856 q^{65} + 21792 q^{66} + 4056 q^{67} + 8224 q^{68} + 4408 q^{69} + 3984 q^{70} + 376 q^{71} - 2624 q^{72} - 3496 q^{73} - 10560 q^{74} - 2244 q^{75} - 23904 q^{76} - 4904 q^{77} - 28256 q^{78} - 32 q^{79} - 10080 q^{80} + 1384 q^{81} - 32 q^{82} + 4856 q^{83} - 32 q^{84} - 568 q^{85} - 96 q^{86} - 2600 q^{87} - 32 q^{88} - 6824 q^{89} - 48 q^{90} - 7272 q^{91} - 32 q^{92} - 8576 q^{93} - 32 q^{94} - 6120 q^{95} - 96 q^{96} - 11968 q^{97} - 32 q^{98} - 10864 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(640))\)

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
640.4.a \(\chi_{640}(1, \cdot)\) 640.4.a.a 1 1
640.4.a.b 1
640.4.a.c 1
640.4.a.d 1
640.4.a.e 2
640.4.a.f 2
640.4.a.g 2
640.4.a.h 2
640.4.a.i 2
640.4.a.j 2
640.4.a.k 2
640.4.a.l 2
640.4.a.m 3
640.4.a.n 3
640.4.a.o 3
640.4.a.p 3
640.4.a.q 4
640.4.a.r 4
640.4.a.s 4
640.4.a.t 4
640.4.c \(\chi_{640}(129, \cdot)\) 640.4.c.a 18 1
640.4.c.b 18
640.4.c.c 18
640.4.c.d 18
640.4.d \(\chi_{640}(321, \cdot)\) 640.4.d.a 4 1
640.4.d.b 4
640.4.d.c 4
640.4.d.d 4
640.4.d.e 4
640.4.d.f 4
640.4.d.g 8
640.4.d.h 8
640.4.d.i 8
640.4.f \(\chi_{640}(449, \cdot)\) 640.4.f.a 2 1
640.4.f.b 2
640.4.f.c 4
640.4.f.d 4
640.4.f.e 4
640.4.f.f 4
640.4.f.g 4
640.4.f.h 8
640.4.f.i 12
640.4.f.j 12
640.4.f.k 16
640.4.j \(\chi_{640}(543, \cdot)\) n/a 136 2
640.4.l \(\chi_{640}(161, \cdot)\) 640.4.l.a 48 2
640.4.l.b 48
640.4.n \(\chi_{640}(127, \cdot)\) n/a 144 2
640.4.o \(\chi_{640}(63, \cdot)\) n/a 144 2
640.4.q \(\chi_{640}(289, \cdot)\) n/a 136 2
640.4.s \(\chi_{640}(223, \cdot)\) n/a 136 2
640.4.u \(\chi_{640}(47, \cdot)\) n/a 280 4
640.4.x \(\chi_{640}(81, \cdot)\) n/a 192 4
640.4.z \(\chi_{640}(49, \cdot)\) n/a 280 4
640.4.ba \(\chi_{640}(207, \cdot)\) n/a 280 4
640.4.bd \(\chi_{640}(87, \cdot)\) None 0 8
640.4.be \(\chi_{640}(41, \cdot)\) None 0 8
640.4.bf \(\chi_{640}(9, \cdot)\) None 0 8
640.4.bj \(\chi_{640}(7, \cdot)\) None 0 8
640.4.bl \(\chi_{640}(3, \cdot)\) n/a 4576 16
640.4.bm \(\chi_{640}(21, \cdot)\) n/a 3072 16
640.4.bo \(\chi_{640}(29, \cdot)\) n/a 4576 16
640.4.br \(\chi_{640}(43, \cdot)\) n/a 4576 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(640))\) into lower level spaces

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