Space of modular forms of level 2142 and weight 4

• Label: 2142.4
• Level: 2142
• Weight: 4
• Dimension: 93736
• Nonzero newspaces: 50
• Sturm bound: 995328
• Trace bound: 18

Defining parameters

Level:	\( N \)	=	\( 2142 = 2 \cdot 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 50 \)
Sturm bound:			\(995328\)
Trace bound:			\(18\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2142))\).

	Total	New	Old
Modular forms	376320	93736	282584
Cusp forms	370176	93736	276440
Eisenstein series	6144	0	6144

Trace form

93736 * q + 16 * q^2 + 12 * q^3 - 32 * q^4 + 96 * q^5 - 72 * q^6 + 88 * q^7 - 32 * q^8 - 420 * q^9 - 328 * q^10 - 424 * q^11 + 96 * q^12 + 628 * q^13 + 1088 * q^14 + 840 * q^15 + 182 * q^17 - 48 * q^18 - 656 * q^19 - 496 * q^20 - 1512 * q^21 - 1912 * q^22 - 3988 * q^23 - 288 * q^24 - 5004 * q^25 - 1592 * q^26 + 1584 * q^27 + 16 * q^28 + 2848 * q^29 + 528 * q^30 + 5684 * q^31 + 256 * q^32 + 4548 * q^33 + 1092 * q^34 + 4832 * q^35 + 2064 * q^36 + 1028 * q^37 + 6320 * q^38 + 5648 * q^39 - 480 * q^40 + 3316 * q^41 + 480 * q^42 - 3988 * q^43 - 3312 * q^44 - 10712 * q^45 - 4752 * q^46 - 22044 * q^47 - 576 * q^48 - 2768 * q^49 - 19616 * q^50 - 16382 * q^51 - 7696 * q^52 - 13948 * q^53 - 6136 * q^54 - 16168 * q^55 + 448 * q^56 + 7532 * q^57 - 2112 * q^58 + 16148 * q^59 + 9440 * q^60 + 880 * q^61 + 21968 * q^62 + 27420 * q^63 + 1024 * q^64 + 45392 * q^65 + 16832 * q^66 + 11440 * q^67 + 1568 * q^68 + 13824 * q^69 - 2424 * q^70 - 1296 * q^71 - 96 * q^72 - 1316 * q^73 - 4480 * q^74 - 10428 * q^75 + 512 * q^76 - 15820 * q^77 - 16560 * q^78 - 3932 * q^79 + 128 * q^80 - 588 * q^81 + 576 * q^82 + 3380 * q^83 + 1488 * q^84 + 41624 * q^85 + 14232 * q^86 + 17544 * q^87 + 9312 * q^88 + 31884 * q^89 + 8448 * q^90 + 19700 * q^91 - 160 * q^92 - 12920 * q^93 + 5232 * q^94 - 34396 * q^95 + 768 * q^96 - 19828 * q^97 - 7128 * q^98 - 29424 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2142))\)

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
2142.4.a	\(\chi_{2142}(1, \cdot)\)	2142.4.a.a	1	1
		2142.4.a.b	1
		2142.4.a.c	1
		2142.4.a.d	1
		2142.4.a.e	1
		2142.4.a.f	1
		2142.4.a.g	1
		2142.4.a.h	1
		2142.4.a.i	2
		2142.4.a.j	2
		2142.4.a.k	2
		2142.4.a.l	2
		2142.4.a.m	2
		2142.4.a.n	3
		2142.4.a.o	3
		2142.4.a.p	3
		2142.4.a.q	3
		2142.4.a.r	3
		2142.4.a.s	3
		2142.4.a.t	3
		2142.4.a.u	3
		2142.4.a.v	3
		2142.4.a.w	4
		2142.4.a.x	4
		2142.4.a.y	4
		2142.4.a.z	4
		2142.4.a.ba	4
		2142.4.a.bb	4
		2142.4.a.bc	4
		2142.4.a.bd	4
		2142.4.a.be	5
		2142.4.a.bf	5
		2142.4.a.bg	5
		2142.4.a.bh	7
		2142.4.a.bi	7
		2142.4.a.bj	7
		2142.4.a.bk	7
2142.4.b	\(\chi_{2142}(883, \cdot)\)	n/a	136	1
2142.4.e	\(\chi_{2142}(2141, \cdot)\)	n/a	144	1
2142.4.f	\(\chi_{2142}(1259, \cdot)\)	n/a	128	1
2142.4.i	\(\chi_{2142}(1633, \cdot)\)	n/a	768	2
2142.4.j	\(\chi_{2142}(715, \cdot)\)	n/a	576	2
2142.4.k	\(\chi_{2142}(613, \cdot)\)	n/a	320	2
2142.4.l	\(\chi_{2142}(205, \cdot)\)	n/a	768	2
2142.4.n	\(\chi_{2142}(251, \cdot)\)	n/a	288	2
2142.4.p	\(\chi_{2142}(1135, \cdot)\)	n/a	272	2
2142.4.r	\(\chi_{2142}(67, \cdot)\)	n/a	864	2
2142.4.s	\(\chi_{2142}(815, \cdot)\)	n/a	864	2
2142.4.y	\(\chi_{2142}(341, \cdot)\)	n/a	256	2
2142.4.ba	\(\chi_{2142}(545, \cdot)\)	n/a	768	2
2142.4.bb	\(\chi_{2142}(1361, \cdot)\)	n/a	768	2
2142.4.bd	\(\chi_{2142}(1223, \cdot)\)	n/a	288	2
2142.4.bf	\(\chi_{2142}(713, \cdot)\)	n/a	864	2
2142.4.bi	\(\chi_{2142}(101, \cdot)\)	n/a	864	2
2142.4.bj	\(\chi_{2142}(373, \cdot)\)	n/a	864	2
2142.4.bm	\(\chi_{2142}(169, \cdot)\)	n/a	648	2
2142.4.bo	\(\chi_{2142}(1495, \cdot)\)	n/a	360	2
2142.4.bq	\(\chi_{2142}(1055, \cdot)\)	n/a	768	2
2142.4.bs	\(\chi_{2142}(127, \cdot)\)	n/a	536	4
2142.4.bu	\(\chi_{2142}(1385, \cdot)\)	n/a	576	4
2142.4.bw	\(\chi_{2142}(89, \cdot)\)	n/a	576	4
2142.4.by	\(\chi_{2142}(421, \cdot)\)	n/a	1296	4
2142.4.ca	\(\chi_{2142}(319, \cdot)\)	n/a	1728	4
2142.4.cd	\(\chi_{2142}(625, \cdot)\)	n/a	1728	4
2142.4.ce	\(\chi_{2142}(47, \cdot)\)	n/a	1728	4
2142.4.ch	\(\chi_{2142}(353, \cdot)\)	n/a	1728	4
2142.4.ci	\(\chi_{2142}(293, \cdot)\)	n/a	1728	4
2142.4.ck	\(\chi_{2142}(361, \cdot)\)	n/a	720	4
2142.4.co	\(\chi_{2142}(181, \cdot)\)	n/a	1440	8
2142.4.cp	\(\chi_{2142}(71, \cdot)\)	n/a	864	8
2142.4.cr	\(\chi_{2142}(739, \cdot)\)	n/a	1440	8
2142.4.cs	\(\chi_{2142}(257, \cdot)\)	n/a	3456	8
2142.4.cv	\(\chi_{2142}(83, \cdot)\)	n/a	3456	8
2142.4.cw	\(\chi_{2142}(59, \cdot)\)	n/a	3456	8
2142.4.cy	\(\chi_{2142}(25, \cdot)\)	n/a	3456	8
2142.4.db	\(\chi_{2142}(43, \cdot)\)	n/a	2592	8
2142.4.dc	\(\chi_{2142}(331, \cdot)\)	n/a	3456	8
2142.4.df	\(\chi_{2142}(467, \cdot)\)	n/a	1152	8
2142.4.dg	\(\chi_{2142}(11, \cdot)\)	n/a	6912	16
2142.4.dh	\(\chi_{2142}(241, \cdot)\)	n/a	6912	16
2142.4.dm	\(\chi_{2142}(107, \cdot)\)	n/a	2304	16
2142.4.dn	\(\chi_{2142}(29, \cdot)\)	n/a	5184	16
2142.4.do	\(\chi_{2142}(73, \cdot)\)	n/a	2880	16
2142.4.dp	\(\chi_{2142}(97, \cdot)\)	n/a	6912	16
2142.4.du	\(\chi_{2142}(31, \cdot)\)	n/a	6912	16
2142.4.dv	\(\chi_{2142}(65, \cdot)\)	n/a	6912	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2142))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2142)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(357))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(714))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1071))\)\(^{\oplus 2}\)