# Properties

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

## 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

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

## 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

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