Space of modular forms of level 2541 and weight 2

• Label: 2541.2
• Level: 2541
• Weight: 2
• Dimension: 162824
• Nonzero newspaces: 32
• Sturm bound: 929280
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(929280\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2541))\).

	Total	New	Old
Modular forms	236160	165636	70524
Cusp forms	228481	162824	65657
Eisenstein series	7679	2812	4867

Trace form

162824 * q - 6 * q^2 - 184 * q^3 - 372 * q^4 - 6 * q^5 - 160 * q^6 - 436 * q^7 + 68 * q^8 - 138 * q^9 - 252 * q^10 + 20 * q^11 - 264 * q^12 - 334 * q^13 + 60 * q^14 - 382 * q^15 - 152 * q^16 + 96 * q^17 - 126 * q^18 - 266 * q^19 + 152 * q^20 - 179 * q^21 - 880 * q^22 + 56 * q^23 - 92 * q^24 - 226 * q^25 + 158 * q^26 - 238 * q^27 - 340 * q^28 + 56 * q^29 - 172 * q^30 - 306 * q^31 + 20 * q^32 - 220 * q^33 - 568 * q^34 + 74 * q^35 - 446 * q^36 - 236 * q^37 + 134 * q^38 - 94 * q^39 - 16 * q^40 + 180 * q^41 - 167 * q^42 - 668 * q^43 + 220 * q^44 - 166 * q^45 + 88 * q^46 + 238 * q^47 + 80 * q^48 - 232 * q^49 + 344 * q^50 + 16 * q^51 + 56 * q^52 + 220 * q^53 - 126 * q^54 - 240 * q^55 + 222 * q^56 - 466 * q^57 - 96 * q^58 + 84 * q^59 - 476 * q^60 - 342 * q^61 - 60 * q^62 - 421 * q^63 - 1100 * q^64 - 198 * q^65 - 450 * q^66 - 790 * q^67 - 440 * q^68 - 464 * q^69 - 906 * q^70 - 324 * q^71 - 932 * q^72 - 464 * q^73 - 246 * q^74 - 526 * q^75 - 1060 * q^76 - 90 * q^77 - 1166 * q^78 - 282 * q^79 - 552 * q^80 - 630 * q^81 - 508 * q^82 + 76 * q^83 - 825 * q^84 - 956 * q^85 - 298 * q^86 - 256 * q^87 - 440 * q^88 - 40 * q^89 - 424 * q^90 - 598 * q^91 + 32 * q^92 - 96 * q^93 - 132 * q^94 + 354 * q^95 - 460 * q^96 + 28 * q^97 + 440 * q^98 - 440 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2541))\)

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
2541.2.a	\(\chi_{2541}(1, \cdot)\)	2541.2.a.a	1	1
		2541.2.a.b	1
		2541.2.a.c	1
		2541.2.a.d	1
		2541.2.a.e	1
		2541.2.a.f	1
		2541.2.a.g	1
		2541.2.a.h	1
		2541.2.a.i	1
		2541.2.a.j	1
		2541.2.a.k	1
		2541.2.a.l	1
		2541.2.a.m	2
		2541.2.a.n	2
		2541.2.a.o	2
		2541.2.a.p	2
		2541.2.a.q	2
		2541.2.a.r	2
		2541.2.a.s	2
		2541.2.a.t	2
		2541.2.a.u	2
		2541.2.a.v	2
		2541.2.a.w	2
		2541.2.a.x	2
		2541.2.a.y	2
		2541.2.a.z	2
		2541.2.a.ba	2
		2541.2.a.bb	2
		2541.2.a.bc	2
		2541.2.a.bd	2
		2541.2.a.be	2
		2541.2.a.bf	2
		2541.2.a.bg	3
		2541.2.a.bh	3
		2541.2.a.bi	3
		2541.2.a.bj	3
		2541.2.a.bk	4
		2541.2.a.bl	4
		2541.2.a.bm	4
		2541.2.a.bn	4
		2541.2.a.bo	4
		2541.2.a.bp	4
		2541.2.a.bq	10
		2541.2.a.br	10
2541.2.c	\(\chi_{2541}(1693, \cdot)\)	n/a	144	1
2541.2.e	\(\chi_{2541}(1574, \cdot)\)	n/a	272	1
2541.2.g	\(\chi_{2541}(1814, \cdot)\)	n/a	216	1
2541.2.i	\(\chi_{2541}(1453, \cdot)\)	n/a	290	2
2541.2.j	\(\chi_{2541}(148, \cdot)\)	n/a	432	4
2541.2.l	\(\chi_{2541}(725, \cdot)\)	n/a	544	2
2541.2.n	\(\chi_{2541}(122, \cdot)\)	n/a	546	2
2541.2.p	\(\chi_{2541}(241, \cdot)\)	n/a	288	2
2541.2.s	\(\chi_{2541}(239, \cdot)\)	n/a	864	4
2541.2.u	\(\chi_{2541}(251, \cdot)\)	n/a	1088	4
2541.2.w	\(\chi_{2541}(118, \cdot)\)	n/a	576	4
2541.2.y	\(\chi_{2541}(232, \cdot)\)	n/a	1320	10
2541.2.z	\(\chi_{2541}(130, \cdot)\)	n/a	1152	8
2541.2.bb	\(\chi_{2541}(197, \cdot)\)	n/a	2640	10
2541.2.bd	\(\chi_{2541}(188, \cdot)\)	n/a	3480	10
2541.2.bf	\(\chi_{2541}(76, \cdot)\)	n/a	1760	10
2541.2.bi	\(\chi_{2541}(40, \cdot)\)	n/a	1152	8
2541.2.bk	\(\chi_{2541}(269, \cdot)\)	n/a	2176	8
2541.2.bm	\(\chi_{2541}(233, \cdot)\)	n/a	2176	8
2541.2.bo	\(\chi_{2541}(67, \cdot)\)	n/a	3520	20
2541.2.bp	\(\chi_{2541}(64, \cdot)\)	n/a	5280	40
2541.2.br	\(\chi_{2541}(10, \cdot)\)	n/a	3520	20
2541.2.bt	\(\chi_{2541}(89, \cdot)\)	n/a	6960	20
2541.2.bv	\(\chi_{2541}(32, \cdot)\)	n/a	6960	20
2541.2.by	\(\chi_{2541}(13, \cdot)\)	n/a	7040	40
2541.2.ca	\(\chi_{2541}(20, \cdot)\)	n/a	13920	40
2541.2.cc	\(\chi_{2541}(8, \cdot)\)	n/a	10560	40
2541.2.ce	\(\chi_{2541}(4, \cdot)\)	n/a	14080	80
2541.2.cg	\(\chi_{2541}(2, \cdot)\)	n/a	27840	80
2541.2.ci	\(\chi_{2541}(5, \cdot)\)	n/a	27840	80
2541.2.ck	\(\chi_{2541}(19, \cdot)\)	n/a	14080	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2541))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2541)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(847))\)\(^{\oplus 2}\)