Space of modular forms of level 1881 and weight 2

• 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 - 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

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}$