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Properties

Label 880.4
Level 880
Weight 4
Dimension 34802
Nonzero newspaces 28
Sturm bound 184320
Trace bound 11

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Defining parameters

Level: \( N \) = \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(184320\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(880))\).

Total New Old
Modular forms 70240 35290 34950
Cusp forms 68000 34802 33198
Eisenstein series 2240 488 1752

Trace form

\( 34802 q - 32 q^{2} - 10 q^{3} + 8 q^{4} - 63 q^{5} - 216 q^{6} - 114 q^{7} - 200 q^{8} - 46 q^{9} + O(q^{10}) \) \( 34802 q - 32 q^{2} - 10 q^{3} + 8 q^{4} - 63 q^{5} - 216 q^{6} - 114 q^{7} - 200 q^{8} - 46 q^{9} - 180 q^{10} + 46 q^{11} + 336 q^{12} + 234 q^{13} + 728 q^{14} - 273 q^{15} + 1032 q^{16} - 78 q^{17} + 672 q^{18} - 758 q^{19} - 436 q^{20} - 820 q^{21} - 1208 q^{22} + 8 q^{23} - 3416 q^{24} - 327 q^{25} - 1144 q^{26} + 890 q^{27} + 72 q^{28} - 610 q^{29} - 836 q^{30} + 1518 q^{31} + 2488 q^{32} + 2910 q^{33} + 2832 q^{34} + 2341 q^{35} + 984 q^{36} + 1882 q^{37} - 808 q^{38} - 1198 q^{39} + 3524 q^{40} - 1406 q^{41} + 2536 q^{42} - 5304 q^{43} + 2768 q^{44} - 938 q^{45} + 4056 q^{46} - 5846 q^{47} + 2824 q^{48} - 1414 q^{49} - 3772 q^{50} - 4570 q^{51} - 8456 q^{52} - 3734 q^{53} - 8984 q^{54} + 1357 q^{55} - 2160 q^{56} + 1566 q^{57} + 8 q^{58} + 5226 q^{59} + 596 q^{60} + 3906 q^{61} - 344 q^{62} + 928 q^{63} + 9752 q^{64} - 4070 q^{65} + 5632 q^{66} - 2416 q^{67} + 2392 q^{68} + 3460 q^{69} - 5000 q^{70} - 2054 q^{71} - 31776 q^{72} - 15430 q^{73} - 29456 q^{74} + 10695 q^{75} - 27976 q^{76} - 3930 q^{77} - 28128 q^{78} + 2254 q^{79} - 11160 q^{80} + 16666 q^{81} + 8152 q^{82} + 13042 q^{83} + 25880 q^{84} + 19473 q^{85} + 37432 q^{86} + 22608 q^{87} + 58088 q^{88} + 16884 q^{89} + 37108 q^{90} + 9078 q^{91} + 34008 q^{92} + 3518 q^{93} + 23256 q^{94} - 8119 q^{95} + 12888 q^{96} - 10470 q^{97} - 1752 q^{98} - 7890 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(880))\)

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
880.4.a \(\chi_{880}(1, \cdot)\) 880.4.a.a 1 1
880.4.a.b 1
880.4.a.c 1
880.4.a.d 1
880.4.a.e 1
880.4.a.f 1
880.4.a.g 1
880.4.a.h 1
880.4.a.i 1
880.4.a.j 1
880.4.a.k 1
880.4.a.l 1
880.4.a.m 1
880.4.a.n 1
880.4.a.o 1
880.4.a.p 1
880.4.a.q 2
880.4.a.r 2
880.4.a.s 2
880.4.a.t 2
880.4.a.u 2
880.4.a.v 3
880.4.a.w 3
880.4.a.x 3
880.4.a.y 3
880.4.a.z 4
880.4.a.ba 4
880.4.a.bb 4
880.4.a.bc 5
880.4.a.bd 5
880.4.b \(\chi_{880}(529, \cdot)\) 880.4.b.a 2 1
880.4.b.b 2
880.4.b.c 2
880.4.b.d 4
880.4.b.e 6
880.4.b.f 6
880.4.b.g 6
880.4.b.h 8
880.4.b.i 10
880.4.b.j 20
880.4.b.k 24
880.4.c \(\chi_{880}(439, \cdot)\) None 0 1
880.4.f \(\chi_{880}(351, \cdot)\) 880.4.f.a 12 1
880.4.f.b 12
880.4.f.c 24
880.4.f.d 24
880.4.g \(\chi_{880}(441, \cdot)\) None 0 1
880.4.l \(\chi_{880}(89, \cdot)\) None 0 1
880.4.m \(\chi_{880}(879, \cdot)\) n/a 108 1
880.4.p \(\chi_{880}(791, \cdot)\) None 0 1
880.4.s \(\chi_{880}(67, \cdot)\) n/a 720 2
880.4.t \(\chi_{880}(197, \cdot)\) n/a 856 2
880.4.v \(\chi_{880}(131, \cdot)\) n/a 576 2
880.4.w \(\chi_{880}(221, \cdot)\) n/a 480 2
880.4.z \(\chi_{880}(23, \cdot)\) None 0 2
880.4.bb \(\chi_{880}(153, \cdot)\) None 0 2
880.4.bd \(\chi_{880}(417, \cdot)\) n/a 212 2
880.4.bf \(\chi_{880}(287, \cdot)\) n/a 180 2
880.4.bh \(\chi_{880}(309, \cdot)\) n/a 720 2
880.4.bi \(\chi_{880}(219, \cdot)\) n/a 856 2
880.4.bk \(\chi_{880}(243, \cdot)\) n/a 720 2
880.4.bl \(\chi_{880}(373, \cdot)\) n/a 856 2
880.4.bo \(\chi_{880}(81, \cdot)\) n/a 288 4
880.4.bp \(\chi_{880}(151, \cdot)\) None 0 4
880.4.bs \(\chi_{880}(79, \cdot)\) n/a 432 4
880.4.bt \(\chi_{880}(9, \cdot)\) None 0 4
880.4.by \(\chi_{880}(201, \cdot)\) None 0 4
880.4.bz \(\chi_{880}(271, \cdot)\) n/a 288 4
880.4.cc \(\chi_{880}(39, \cdot)\) None 0 4
880.4.cd \(\chi_{880}(49, \cdot)\) n/a 424 4
880.4.cg \(\chi_{880}(237, \cdot)\) n/a 3424 8
880.4.ch \(\chi_{880}(3, \cdot)\) n/a 3424 8
880.4.ci \(\chi_{880}(19, \cdot)\) n/a 3424 8
880.4.cl \(\chi_{880}(69, \cdot)\) n/a 3424 8
880.4.cm \(\chi_{880}(17, \cdot)\) n/a 848 8
880.4.co \(\chi_{880}(47, \cdot)\) n/a 864 8
880.4.cq \(\chi_{880}(103, \cdot)\) None 0 8
880.4.cs \(\chi_{880}(57, \cdot)\) None 0 8
880.4.cu \(\chi_{880}(141, \cdot)\) n/a 2304 8
880.4.cx \(\chi_{880}(51, \cdot)\) n/a 2304 8
880.4.cy \(\chi_{880}(13, \cdot)\) n/a 3424 8
880.4.cz \(\chi_{880}(147, \cdot)\) n/a 3424 8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(880))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(880)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(880))\)\(^{\oplus 1}\)