Space of modular forms of level 2775 and weight 2

• Label: 2775.2
• Level: 2775
• Weight: 2
• Dimension: 187412
• Nonzero newspaces: 60
• Sturm bound: 1094400
• Trace bound: 8

Defining parameters

Level:	$N$	=	$2775 = 3 \cdot 5^{2} \cdot 37$
Weight:	$k$	=	$2$
Nonzero newspaces:			$60$
Sturm bound:			$1094400$
Trace bound:			$8$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(2775))$.

	Total	New	Old
Modular forms	277632	190284	87348
Cusp forms	269569	187412	82157
Eisenstein series	8063	2872	5191

Trace form

187412 * q + 2 * q^2 - 216 * q^3 - 418 * q^4 + 12 * q^5 - 332 * q^6 - 412 * q^7 + 42 * q^8 - 208 * q^9 - 508 * q^10 + 8 * q^11 - 196 * q^12 - 408 * q^13 + 48 * q^14 - 260 * q^15 - 690 * q^16 + 4 * q^17 - 232 * q^18 - 452 * q^19 - 72 * q^20 - 366 * q^21 - 500 * q^22 - 32 * q^23 - 336 * q^24 - 604 * q^25 + 30 * q^26 - 210 * q^27 - 436 * q^28 + 8 * q^29 - 316 * q^30 - 592 * q^31 + 110 * q^32 - 178 * q^33 - 284 * q^34 + 40 * q^35 - 324 * q^36 - 356 * q^37 + 56 * q^38 - 216 * q^39 - 580 * q^40 + 152 * q^41 - 294 * q^42 - 412 * q^43 + 48 * q^44 - 416 * q^45 - 636 * q^46 + 4 * q^47 - 308 * q^48 - 514 * q^49 - 212 * q^50 - 774 * q^51 - 664 * q^52 - 112 * q^53 - 464 * q^54 - 584 * q^55 - 350 * q^57 - 484 * q^58 + 16 * q^59 - 316 * q^60 - 558 * q^61 + 172 * q^62 - 70 * q^63 - 14 * q^64 + 116 * q^65 - 10 * q^66 - 172 * q^67 + 460 * q^68 + 118 * q^69 - 296 * q^70 + 256 * q^71 + 324 * q^72 - 60 * q^73 + 422 * q^74 - 348 * q^75 - 868 * q^76 + 336 * q^77 + 254 * q^78 - 124 * q^79 + 308 * q^80 - 112 * q^81 - 160 * q^82 + 128 * q^83 + 230 * q^84 - 652 * q^85 + 260 * q^86 - 98 * q^87 - 416 * q^88 - 54 * q^89 - 240 * q^90 - 708 * q^91 - 28 * q^92 - 424 * q^93 - 812 * q^94 - 112 * q^95 - 624 * q^96 - 784 * q^97 - 190 * q^98 - 316 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(2775))$

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
2775.2.a	$\chi_{2775}(1, \cdot)$	2775.2.a.a	1	1
		2775.2.a.b	1
		2775.2.a.c	1
		2775.2.a.d	1
		2775.2.a.e	1
		2775.2.a.f	1
		2775.2.a.g	1
		2775.2.a.h	1
		2775.2.a.i	1
		2775.2.a.j	1
		2775.2.a.k	2
		2775.2.a.l	2
		2775.2.a.m	2
		2775.2.a.n	2
		2775.2.a.o	2
		2775.2.a.p	2
		2775.2.a.q	2
		2775.2.a.r	3
		2775.2.a.s	3
		2775.2.a.t	3
		2775.2.a.u	3
		2775.2.a.v	3
		2775.2.a.w	4
		2775.2.a.x	4
		2775.2.a.y	4
		2775.2.a.z	5
		2775.2.a.ba	5
		2775.2.a.bb	5
		2775.2.a.bc	5
		2775.2.a.bd	5
		2775.2.a.be	6
		2775.2.a.bf	6
		2775.2.a.bg	13
		2775.2.a.bh	13
2775.2.c	$\chi_{2775}(1999, \cdot)$	n/a	108	1
2775.2.e	$\chi_{2775}(2626, \cdot)$	n/a	122	1
2775.2.g	$\chi_{2775}(1849, \cdot)$	n/a	112	1
2775.2.i	$\chi_{2775}(676, \cdot)$	n/a	240	2
2775.2.j	$\chi_{2775}(43, \cdot)$	n/a	228	2
2775.2.m	$\chi_{2775}(524, \cdot)$	n/a	448	2
2775.2.n	$\chi_{2775}(332, \cdot)$	n/a	448	2
2775.2.o	$\chi_{2775}(482, \cdot)$	n/a	432	2
2775.2.s	$\chi_{2775}(401, \cdot)$	n/a	468	2
2775.2.t	$\chi_{2775}(1918, \cdot)$	n/a	228	2
2775.2.v	$\chi_{2775}(556, \cdot)$	n/a	720	4
2775.2.y	$\chi_{2775}(1174, \cdot)$	n/a	224	2
2775.2.ba	$\chi_{2775}(751, \cdot)$	n/a	244	2
2775.2.bc	$\chi_{2775}(1099, \cdot)$	n/a	232	2
2775.2.bd	$\chi_{2775}(451, \cdot)$	n/a	714	6
2775.2.be	$\chi_{2775}(184, \cdot)$	n/a	768	4
2775.2.bh	$\chi_{2775}(334, \cdot)$	n/a	720	4
2775.2.bj	$\chi_{2775}(406, \cdot)$	n/a	752	4
2775.2.bl	$\chi_{2775}(82, \cdot)$	n/a	456	4
2775.2.bo	$\chi_{2775}(251, \cdot)$	n/a	936	4
2775.2.bp	$\chi_{2775}(1232, \cdot)$	n/a	896	4
2775.2.bq	$\chi_{2775}(1157, \cdot)$	n/a	896	4
2775.2.bu	$\chi_{2775}(674, \cdot)$	n/a	896	4
2775.2.bv	$\chi_{2775}(193, \cdot)$	n/a	456	4
2775.2.bx	$\chi_{2775}(121, \cdot)$	n/a	1536	8
2775.2.by	$\chi_{2775}(724, \cdot)$	n/a	672	6
2775.2.cb	$\chi_{2775}(49, \cdot)$	n/a	696	6
2775.2.cc	$\chi_{2775}(151, \cdot)$	n/a	726	6
2775.2.cg	$\chi_{2775}(253, \cdot)$	n/a	1520	8
2775.2.ch	$\chi_{2775}(179, \cdot)$	n/a	3008	8
2775.2.cl	$\chi_{2775}(38, \cdot)$	n/a	2880	8
2775.2.cm	$\chi_{2775}(887, \cdot)$	n/a	3008	8
2775.2.cn	$\chi_{2775}(191, \cdot)$	n/a	3008	8
2775.2.cq	$\chi_{2775}(142, \cdot)$	n/a	1520	8
2775.2.cr	$\chi_{2775}(196, \cdot)$	n/a	1504	8
2775.2.ct	$\chi_{2775}(454, \cdot)$	n/a	1504	8
2775.2.cw	$\chi_{2775}(64, \cdot)$	n/a	1536	8
2775.2.cz	$\chi_{2775}(457, \cdot)$	n/a	1368	12
2775.2.db	$\chi_{2775}(476, \cdot)$	n/a	2820	12
2775.2.dc	$\chi_{2775}(224, \cdot)$	n/a	2688	12
2775.2.de	$\chi_{2775}(107, \cdot)$	n/a	2688	12
2775.2.dh	$\chi_{2775}(632, \cdot)$	n/a	2688	12
2775.2.dj	$\chi_{2775}(568, \cdot)$	n/a	1368	12
2775.2.dk	$\chi_{2775}(16, \cdot)$	n/a	4608	24
2775.2.dm	$\chi_{2775}(208, \cdot)$	n/a	3040	16
2775.2.dn	$\chi_{2775}(236, \cdot)$	n/a	6016	16
2775.2.dr	$\chi_{2775}(47, \cdot)$	n/a	6016	16
2775.2.ds	$\chi_{2775}(122, \cdot)$	n/a	6016	16
2775.2.dt	$\chi_{2775}(14, \cdot)$	n/a	6016	16
2775.2.dw	$\chi_{2775}(88, \cdot)$	n/a	3040	16
2775.2.dz	$\chi_{2775}(136, \cdot)$	n/a	4512	24
2775.2.ea	$\chi_{2775}(34, \cdot)$	n/a	4512	24
2775.2.ed	$\chi_{2775}(4, \cdot)$	n/a	4608	24
2775.2.ee	$\chi_{2775}(13, \cdot)$	n/a	9120	48
2775.2.eg	$\chi_{2775}(62, \cdot)$	n/a	18048	48
2775.2.ej	$\chi_{2775}(53, \cdot)$	n/a	18048	48
2775.2.el	$\chi_{2775}(59, \cdot)$	n/a	18048	48
2775.2.em	$\chi_{2775}(56, \cdot)$	n/a	18048	48
2775.2.eo	$\chi_{2775}(22, \cdot)$	n/a	9120	48

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(2775))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(2775)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(111))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(185))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(555))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(925))$$^{\oplus 2}$