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Properties

Label 1280.4
Level 1280
Weight 4
Dimension 75720
Nonzero newspaces 22
Sturm bound 393216
Trace bound 50

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Defining parameters

Level: \( N \) = \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 22 \)
Sturm bound: \(393216\)
Trace bound: \(50\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1280))\).

Total New Old
Modular forms 148864 76344 72520
Cusp forms 146048 75720 70328
Eisenstein series 2816 624 2192

Trace form

\( 75720 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 96 q^{5} - 192 q^{6} - 48 q^{7} - 64 q^{8} - 80 q^{9} + O(q^{10}) \) \( 75720 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 96 q^{5} - 192 q^{6} - 48 q^{7} - 64 q^{8} - 80 q^{9} - 96 q^{10} - 144 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 72 q^{15} - 192 q^{16} - 96 q^{17} - 64 q^{18} - 48 q^{19} - 96 q^{20} - 192 q^{21} - 64 q^{22} - 48 q^{23} - 64 q^{24} - 120 q^{25} - 192 q^{26} - 48 q^{27} - 64 q^{28} - 64 q^{29} - 96 q^{30} - 128 q^{31} - 64 q^{32} - 112 q^{33} - 64 q^{34} - 72 q^{35} - 192 q^{36} - 64 q^{37} - 64 q^{38} - 48 q^{39} - 96 q^{40} - 240 q^{41} - 64 q^{42} - 48 q^{43} - 64 q^{44} + 120 q^{45} - 192 q^{46} - 48 q^{47} - 64 q^{48} + 2648 q^{49} - 96 q^{50} + 5808 q^{51} - 64 q^{52} + 2944 q^{53} - 64 q^{54} + 504 q^{55} - 192 q^{56} - 2768 q^{57} - 64 q^{58} - 5552 q^{59} - 96 q^{60} - 7488 q^{61} - 64 q^{62} - 10144 q^{63} - 64 q^{64} - 4120 q^{65} - 192 q^{66} - 8208 q^{67} - 64 q^{68} - 4288 q^{69} - 96 q^{70} - 1040 q^{71} - 64 q^{72} + 3376 q^{73} - 64 q^{74} + 4344 q^{75} - 192 q^{76} + 7552 q^{77} - 64 q^{78} + 11280 q^{79} - 96 q^{80} + 5544 q^{81} - 64 q^{82} - 48 q^{83} - 64 q^{84} + 904 q^{85} - 192 q^{86} - 48 q^{87} - 64 q^{88} - 80 q^{89} - 96 q^{90} - 144 q^{91} - 64 q^{92} - 928 q^{93} - 64 q^{94} - 64 q^{95} - 192 q^{96} - 112 q^{97} - 64 q^{98} + 384 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1280))\)

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
1280.4.a \(\chi_{1280}(1, \cdot)\) 1280.4.a.a 2 1
1280.4.a.b 2
1280.4.a.c 2
1280.4.a.d 2
1280.4.a.e 2
1280.4.a.f 2
1280.4.a.g 2
1280.4.a.h 2
1280.4.a.i 2
1280.4.a.j 2
1280.4.a.k 2
1280.4.a.l 2
1280.4.a.m 2
1280.4.a.n 2
1280.4.a.o 2
1280.4.a.p 2
1280.4.a.q 4
1280.4.a.r 4
1280.4.a.s 4
1280.4.a.t 4
1280.4.a.u 4
1280.4.a.v 4
1280.4.a.w 4
1280.4.a.x 4
1280.4.a.y 4
1280.4.a.z 4
1280.4.a.ba 6
1280.4.a.bb 6
1280.4.a.bc 6
1280.4.a.bd 6
1280.4.c \(\chi_{1280}(769, \cdot)\) n/a 140 1
1280.4.d \(\chi_{1280}(641, \cdot)\) 1280.4.d.a 2 1
1280.4.d.b 2
1280.4.d.c 2
1280.4.d.d 2
1280.4.d.e 2
1280.4.d.f 2
1280.4.d.g 2
1280.4.d.h 2
1280.4.d.i 2
1280.4.d.j 2
1280.4.d.k 2
1280.4.d.l 2
1280.4.d.m 2
1280.4.d.n 2
1280.4.d.o 2
1280.4.d.p 2
1280.4.d.q 4
1280.4.d.r 4
1280.4.d.s 4
1280.4.d.t 4
1280.4.d.u 4
1280.4.d.v 4
1280.4.d.w 4
1280.4.d.x 4
1280.4.d.y 4
1280.4.d.z 6
1280.4.d.ba 6
1280.4.d.bb 8
1280.4.d.bc 8
1280.4.f \(\chi_{1280}(129, \cdot)\) n/a 140 1
1280.4.j \(\chi_{1280}(63, \cdot)\) n/a 288 2
1280.4.l \(\chi_{1280}(321, \cdot)\) n/a 192 2
1280.4.n \(\chi_{1280}(767, \cdot)\) n/a 280 2
1280.4.o \(\chi_{1280}(127, \cdot)\) n/a 280 2
1280.4.q \(\chi_{1280}(449, \cdot)\) n/a 288 2
1280.4.s \(\chi_{1280}(703, \cdot)\) n/a 288 2
1280.4.u \(\chi_{1280}(543, \cdot)\) n/a 560 4
1280.4.x \(\chi_{1280}(161, \cdot)\) n/a 384 4
1280.4.z \(\chi_{1280}(289, \cdot)\) n/a 560 4
1280.4.ba \(\chi_{1280}(223, \cdot)\) n/a 560 4
1280.4.bd \(\chi_{1280}(47, \cdot)\) n/a 1136 8
1280.4.be \(\chi_{1280}(81, \cdot)\) n/a 768 8
1280.4.bf \(\chi_{1280}(49, \cdot)\) n/a 1136 8
1280.4.bj \(\chi_{1280}(207, \cdot)\) n/a 1136 8
1280.4.bl \(\chi_{1280}(7, \cdot)\) None 0 16
1280.4.bm \(\chi_{1280}(41, \cdot)\) None 0 16
1280.4.bo \(\chi_{1280}(9, \cdot)\) None 0 16
1280.4.br \(\chi_{1280}(87, \cdot)\) None 0 16
1280.4.bt \(\chi_{1280}(3, \cdot)\) n/a 18368 32
1280.4.bv \(\chi_{1280}(21, \cdot)\) n/a 12288 32
1280.4.bw \(\chi_{1280}(29, \cdot)\) n/a 18368 32
1280.4.by \(\chi_{1280}(43, \cdot)\) n/a 18368 32

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1280))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1280)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(640))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1280))\)\(^{\oplus 1}\)