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Properties

Label 880.3
Level 880
Weight 3
Dimension 23122
Nonzero newspaces 28
Sturm bound 138240
Trace bound 11

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Defining parameters

Level: \( N \) = \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(138240\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(880))\).

Total New Old
Modular forms 47200 23606 23594
Cusp forms 44960 23122 21838
Eisenstein series 2240 484 1756

Trace form

\( 23122 q - 32 q^{2} - 26 q^{3} - 56 q^{4} - 71 q^{5} - 120 q^{6} - 34 q^{7} - 8 q^{8} + 26 q^{9} + O(q^{10}) \) \( 23122 q - 32 q^{2} - 26 q^{3} - 56 q^{4} - 71 q^{5} - 120 q^{6} - 34 q^{7} - 8 q^{8} + 26 q^{9} + 28 q^{10} - 114 q^{11} + 144 q^{12} - 46 q^{13} + 24 q^{14} - 129 q^{15} - 248 q^{16} - 222 q^{17} - 320 q^{18} + 106 q^{19} - 212 q^{20} - 136 q^{21} - 136 q^{22} + 288 q^{23} + 168 q^{24} + 57 q^{25} + 296 q^{26} + 466 q^{27} + 456 q^{28} + 302 q^{29} + 636 q^{30} + 62 q^{31} + 568 q^{32} - 270 q^{33} + 272 q^{34} - 377 q^{35} + 88 q^{36} - 206 q^{37} + 248 q^{38} - 1262 q^{39} - 124 q^{40} - 238 q^{41} - 600 q^{42} - 592 q^{43} - 272 q^{44} - 566 q^{45} - 872 q^{46} - 258 q^{47} - 1272 q^{48} - 526 q^{49} - 732 q^{50} + 942 q^{51} - 456 q^{52} + 530 q^{53} - 472 q^{54} + 427 q^{55} - 880 q^{56} + 390 q^{57} - 728 q^{58} + 810 q^{59} - 620 q^{60} - 14 q^{61} - 600 q^{62} + 1304 q^{63} - 488 q^{64} + 296 q^{65} - 544 q^{66} + 872 q^{67} - 808 q^{68} + 552 q^{69} - 392 q^{70} + 1070 q^{71} + 1504 q^{72} + 2194 q^{73} + 1328 q^{74} + 1375 q^{75} + 2296 q^{76} + 1282 q^{77} + 3680 q^{78} + 770 q^{79} + 2120 q^{80} + 1522 q^{81} + 3608 q^{82} + 470 q^{83} + 3864 q^{84} - 647 q^{85} + 2200 q^{86} - 972 q^{87} + 104 q^{88} - 892 q^{89} + 1316 q^{90} - 2482 q^{91} - 168 q^{92} - 3098 q^{93} - 1512 q^{94} - 2445 q^{95} - 1832 q^{96} - 2222 q^{97} - 3128 q^{98} - 2322 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(880))\)

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
880.3.d \(\chi_{880}(681, \cdot)\) None 0 1
880.3.e \(\chi_{880}(111, \cdot)\) 880.3.e.a 16 1
880.3.e.b 24
880.3.h \(\chi_{880}(199, \cdot)\) None 0 1
880.3.i \(\chi_{880}(769, \cdot)\) 880.3.i.a 2 1
880.3.i.b 2
880.3.i.c 2
880.3.i.d 4
880.3.i.e 4
880.3.i.f 4
880.3.i.g 8
880.3.i.h 8
880.3.i.i 36
880.3.j \(\chi_{880}(241, \cdot)\) 880.3.j.a 8 1
880.3.j.b 8
880.3.j.c 8
880.3.j.d 24
880.3.k \(\chi_{880}(551, \cdot)\) None 0 1
880.3.n \(\chi_{880}(639, \cdot)\) 880.3.n.a 20 1
880.3.n.b 40
880.3.o \(\chi_{880}(329, \cdot)\) None 0 1
880.3.q \(\chi_{880}(43, \cdot)\) n/a 568 2
880.3.r \(\chi_{880}(573, \cdot)\) n/a 480 2
880.3.u \(\chi_{880}(419, \cdot)\) n/a 480 2
880.3.x \(\chi_{880}(109, \cdot)\) n/a 568 2
880.3.y \(\chi_{880}(527, \cdot)\) n/a 144 2
880.3.ba \(\chi_{880}(177, \cdot)\) n/a 120 2
880.3.bc \(\chi_{880}(617, \cdot)\) None 0 2
880.3.be \(\chi_{880}(87, \cdot)\) None 0 2
880.3.bg \(\chi_{880}(21, \cdot)\) n/a 384 2
880.3.bj \(\chi_{880}(331, \cdot)\) n/a 320 2
880.3.bm \(\chi_{880}(483, \cdot)\) n/a 568 2
880.3.bn \(\chi_{880}(133, \cdot)\) n/a 480 2
880.3.bq \(\chi_{880}(249, \cdot)\) None 0 4
880.3.br \(\chi_{880}(159, \cdot)\) n/a 288 4
880.3.bu \(\chi_{880}(71, \cdot)\) None 0 4
880.3.bv \(\chi_{880}(161, \cdot)\) n/a 192 4
880.3.bw \(\chi_{880}(129, \cdot)\) n/a 280 4
880.3.bx \(\chi_{880}(119, \cdot)\) None 0 4
880.3.ca \(\chi_{880}(31, \cdot)\) n/a 192 4
880.3.cb \(\chi_{880}(41, \cdot)\) None 0 4
880.3.ce \(\chi_{880}(53, \cdot)\) n/a 2272 8
880.3.cf \(\chi_{880}(83, \cdot)\) n/a 2272 8
880.3.cj \(\chi_{880}(91, \cdot)\) n/a 1536 8
880.3.ck \(\chi_{880}(61, \cdot)\) n/a 1536 8
880.3.cn \(\chi_{880}(137, \cdot)\) None 0 8
880.3.cp \(\chi_{880}(7, \cdot)\) None 0 8
880.3.cr \(\chi_{880}(63, \cdot)\) n/a 576 8
880.3.ct \(\chi_{880}(97, \cdot)\) n/a 560 8
880.3.cv \(\chi_{880}(29, \cdot)\) n/a 2272 8
880.3.cw \(\chi_{880}(59, \cdot)\) n/a 2272 8
880.3.da \(\chi_{880}(37, \cdot)\) n/a 2272 8
880.3.db \(\chi_{880}(123, \cdot)\) n/a 2272 8

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(880))\) into lower level spaces

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