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Properties

Label 1881.2
Level 1881
Weight 2
Dimension 98952
Nonzero newspaces 64
Sturm bound 518400
Trace bound 22

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Defining parameters

Level: \( N \) = \( 1881 = 3^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(518400\)
Trace bound: \(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1881))\).

Total New Old
Modular forms 132480 101708 30772
Cusp forms 126721 98952 27769
Eisenstein series 5759 2756 3003

Trace form

\( 98952 q - 186 q^{2} - 248 q^{3} - 186 q^{4} - 186 q^{5} - 248 q^{6} - 176 q^{7} - 166 q^{8} - 248 q^{9} + O(q^{10}) \) \( 98952 q - 186 q^{2} - 248 q^{3} - 186 q^{4} - 186 q^{5} - 248 q^{6} - 176 q^{7} - 166 q^{8} - 248 q^{9} - 528 q^{10} - 203 q^{11} - 568 q^{12} - 152 q^{13} - 120 q^{14} - 248 q^{15} - 54 q^{16} - 138 q^{17} - 248 q^{18} - 546 q^{19} - 340 q^{20} - 248 q^{21} - 126 q^{22} - 418 q^{23} - 308 q^{24} - 170 q^{25} - 220 q^{26} - 308 q^{27} - 610 q^{28} - 220 q^{29} - 368 q^{30} - 190 q^{31} - 316 q^{32} - 384 q^{33} - 416 q^{34} - 224 q^{35} - 460 q^{36} - 524 q^{37} - 140 q^{38} - 596 q^{39} - 94 q^{40} - 180 q^{41} - 368 q^{42} - 122 q^{43} - 229 q^{44} - 696 q^{45} - 554 q^{46} - 242 q^{47} - 580 q^{48} - 166 q^{49} - 604 q^{50} - 448 q^{51} - 572 q^{52} - 452 q^{53} - 624 q^{54} - 787 q^{55} - 1308 q^{56} - 528 q^{57} - 768 q^{58} - 636 q^{59} - 960 q^{60} - 412 q^{61} - 810 q^{62} - 552 q^{63} - 1110 q^{64} - 558 q^{65} - 688 q^{66} - 598 q^{67} - 788 q^{68} - 516 q^{69} - 396 q^{70} - 456 q^{71} - 656 q^{72} - 444 q^{73} - 480 q^{74} - 388 q^{75} - 46 q^{76} - 507 q^{77} - 768 q^{78} + 28 q^{79} + 60 q^{80} - 248 q^{81} - 286 q^{82} + 130 q^{83} - 68 q^{84} + 160 q^{85} + 302 q^{86} - 48 q^{87} + 109 q^{88} - 34 q^{89} - 28 q^{90} - 400 q^{91} + 458 q^{92} - 48 q^{93} + 54 q^{94} - 168 q^{95} - 244 q^{96} - 228 q^{97} - 116 q^{98} - 90 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1881))\)

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
1881.2.a \(\chi_{1881}(1, \cdot)\) 1881.2.a.a 1 1
1881.2.a.b 1
1881.2.a.c 1
1881.2.a.d 2
1881.2.a.e 3
1881.2.a.f 3
1881.2.a.g 3
1881.2.a.h 3
1881.2.a.i 3
1881.2.a.j 4
1881.2.a.k 5
1881.2.a.l 5
1881.2.a.m 5
1881.2.a.n 7
1881.2.a.o 7
1881.2.a.p 7
1881.2.a.q 7
1881.2.a.r 7
1881.2.f \(\chi_{1881}(989, \cdot)\) 1881.2.f.a 72 1
1881.2.g \(\chi_{1881}(683, \cdot)\) 1881.2.g.a 64 1
1881.2.h \(\chi_{1881}(208, \cdot)\) 1881.2.h.a 2 1
1881.2.h.b 4
1881.2.h.c 4
1881.2.h.d 8
1881.2.h.e 8
1881.2.h.f 16
1881.2.h.g 24
1881.2.h.h 32
1881.2.i \(\chi_{1881}(628, \cdot)\) n/a 360 2
1881.2.j \(\chi_{1881}(1090, \cdot)\) n/a 164 2
1881.2.k \(\chi_{1881}(463, \cdot)\) n/a 400 2
1881.2.l \(\chi_{1881}(562, \cdot)\) n/a 400 2
1881.2.m \(\chi_{1881}(685, \cdot)\) n/a 360 4
1881.2.r \(\chi_{1881}(221, \cdot)\) n/a 400 2
1881.2.s \(\chi_{1881}(824, \cdot)\) n/a 472 2
1881.2.t \(\chi_{1881}(901, \cdot)\) n/a 196 2
1881.2.u \(\chi_{1881}(835, \cdot)\) n/a 472 2
1881.2.v \(\chi_{1881}(197, \cdot)\) n/a 160 2
1881.2.w \(\chi_{1881}(56, \cdot)\) n/a 400 2
1881.2.x \(\chi_{1881}(362, \cdot)\) n/a 432 2
1881.2.y \(\chi_{1881}(1376, \cdot)\) n/a 128 2
1881.2.z \(\chi_{1881}(373, \cdot)\) n/a 472 2
1881.2.bm \(\chi_{1881}(274, \cdot)\) n/a 472 2
1881.2.bn \(\chi_{1881}(122, \cdot)\) n/a 400 2
1881.2.bo \(\chi_{1881}(923, \cdot)\) n/a 472 2
1881.2.bp \(\chi_{1881}(232, \cdot)\) n/a 1200 6
1881.2.bq \(\chi_{1881}(100, \cdot)\) n/a 504 6
1881.2.br \(\chi_{1881}(529, \cdot)\) n/a 1200 6
1881.2.bs \(\chi_{1881}(721, \cdot)\) n/a 392 4
1881.2.bt \(\chi_{1881}(170, \cdot)\) n/a 320 4
1881.2.bu \(\chi_{1881}(134, \cdot)\) n/a 288 4
1881.2.bz \(\chi_{1881}(49, \cdot)\) n/a 1888 8
1881.2.ca \(\chi_{1881}(619, \cdot)\) n/a 1888 8
1881.2.cb \(\chi_{1881}(64, \cdot)\) n/a 784 8
1881.2.cc \(\chi_{1881}(58, \cdot)\) n/a 1728 8
1881.2.cd \(\chi_{1881}(439, \cdot)\) n/a 1416 6
1881.2.ce \(\chi_{1881}(263, \cdot)\) n/a 1416 6
1881.2.ch \(\chi_{1881}(89, \cdot)\) n/a 408 6
1881.2.ci \(\chi_{1881}(452, \cdot)\) n/a 1200 6
1881.2.cn \(\chi_{1881}(593, \cdot)\) n/a 480 6
1881.2.co \(\chi_{1881}(241, \cdot)\) n/a 1416 6
1881.2.cp \(\chi_{1881}(131, \cdot)\) n/a 1416 6
1881.2.cq \(\chi_{1881}(10, \cdot)\) n/a 588 6
1881.2.cv \(\chi_{1881}(155, \cdot)\) n/a 1200 6
1881.2.cy \(\chi_{1881}(68, \cdot)\) n/a 1888 8
1881.2.cz \(\chi_{1881}(335, \cdot)\) n/a 1888 8
1881.2.da \(\chi_{1881}(259, \cdot)\) n/a 1888 8
1881.2.dn \(\chi_{1881}(160, \cdot)\) n/a 1888 8
1881.2.do \(\chi_{1881}(179, \cdot)\) n/a 640 8
1881.2.dp \(\chi_{1881}(248, \cdot)\) n/a 1728 8
1881.2.dq \(\chi_{1881}(113, \cdot)\) n/a 1888 8
1881.2.dr \(\chi_{1881}(710, \cdot)\) n/a 640 8
1881.2.ds \(\chi_{1881}(94, \cdot)\) n/a 1888 8
1881.2.dt \(\chi_{1881}(46, \cdot)\) n/a 784 8
1881.2.du \(\chi_{1881}(140, \cdot)\) n/a 1888 8
1881.2.dv \(\chi_{1881}(236, \cdot)\) n/a 1888 8
1881.2.ea \(\chi_{1881}(4, \cdot)\) n/a 5664 24
1881.2.eb \(\chi_{1881}(82, \cdot)\) n/a 2352 24
1881.2.ec \(\chi_{1881}(25, \cdot)\) n/a 5664 24
1881.2.ef \(\chi_{1881}(86, \cdot)\) n/a 5664 24
1881.2.ek \(\chi_{1881}(127, \cdot)\) n/a 2352 24
1881.2.el \(\chi_{1881}(101, \cdot)\) n/a 5664 24
1881.2.em \(\chi_{1881}(40, \cdot)\) n/a 5664 24
1881.2.en \(\chi_{1881}(17, \cdot)\) n/a 1920 24
1881.2.es \(\chi_{1881}(14, \cdot)\) n/a 5664 24
1881.2.et \(\chi_{1881}(53, \cdot)\) n/a 1920 24
1881.2.ew \(\chi_{1881}(74, \cdot)\) n/a 5664 24
1881.2.ex \(\chi_{1881}(13, \cdot)\) n/a 5664 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1881))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1881)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(627))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1881))\)\(^{\oplus 1}\)