Space of modular forms of level 1980 and weight 4

• Label: 1980.4
• Level: 1980
• Weight: 4
• Dimension: 128988
• Nonzero newspaces: 48
• Sturm bound: 829440
• Trace bound: 24

Defining parameters

Level:	\( N \)	=	\( 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(829440\)
Trace bound:			\(24\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1980))\).

	Total	New	Old
Modular forms	314240	129956	184284
Cusp forms	307840	128988	178852
Eisenstein series	6400	968	5432

Trace form

128988 * q - 30 * q^2 - 12 * q^3 + 22 * q^4 - 68 * q^5 - 4 * q^6 + 60 * q^7 + 66 * q^8 + 4 * q^9 - 264 * q^10 - 18 * q^11 - 88 * q^12 + 332 * q^13 - 668 * q^14 - 24 * q^15 + 250 * q^16 - 48 * q^17 - 440 * q^18 + 226 * q^19 + 362 * q^20 - 920 * q^21 + 808 * q^22 - 1000 * q^23 + 44 * q^24 - 3192 * q^25 - 1280 * q^26 + 1608 * q^27 - 1412 * q^28 + 1724 * q^29 - 1488 * q^30 - 636 * q^31 + 340 * q^32 + 1434 * q^33 + 632 * q^34 + 1404 * q^35 + 4836 * q^36 + 1900 * q^37 + 4380 * q^38 + 88 * q^39 + 890 * q^40 + 1336 * q^41 + 4576 * q^42 - 1512 * q^43 - 3040 * q^44 - 592 * q^45 - 1836 * q^46 + 2168 * q^47 - 9380 * q^48 - 1662 * q^49 - 3808 * q^50 - 3400 * q^51 + 8644 * q^52 - 2108 * q^53 + 1628 * q^54 + 1374 * q^55 + 6264 * q^56 + 388 * q^57 + 4792 * q^58 - 5638 * q^59 - 468 * q^60 - 9568 * q^61 - 15904 * q^62 - 6432 * q^63 - 17258 * q^64 - 8612 * q^65 - 9824 * q^66 - 14392 * q^67 - 2012 * q^68 - 2544 * q^69 + 386 * q^70 + 4304 * q^71 - 976 * q^72 + 7024 * q^73 + 5812 * q^74 - 2392 * q^75 + 11360 * q^76 + 21460 * q^77 + 17336 * q^78 + 20596 * q^79 + 9346 * q^80 + 42532 * q^81 + 16274 * q^82 + 23382 * q^83 + 860 * q^84 - 13578 * q^85 - 24246 * q^86 + 6408 * q^87 - 23204 * q^88 - 7680 * q^89 + 4608 * q^90 - 3792 * q^91 - 13236 * q^92 - 9248 * q^93 - 20060 * q^94 - 2474 * q^95 - 2692 * q^96 - 7986 * q^97 + 1580 * q^98 - 32780 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1980))\)

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
1980.4.a	\(\chi_{1980}(1, \cdot)\)	1980.4.a.a	1	1
		1980.4.a.b	1
		1980.4.a.c	1
		1980.4.a.d	1
		1980.4.a.e	2
		1980.4.a.f	2
		1980.4.a.g	2
		1980.4.a.h	2
		1980.4.a.i	2
		1980.4.a.j	3
		1980.4.a.k	3
		1980.4.a.l	3
		1980.4.a.m	3
		1980.4.a.n	4
		1980.4.a.o	5
		1980.4.a.p	5
		1980.4.a.q	5
		1980.4.a.r	5
1980.4.c	\(\chi_{1980}(1189, \cdot)\)	1980.4.c.a	2	1
		1980.4.c.b	6
		1980.4.c.c	6
		1980.4.c.d	14
		1980.4.c.e	14
		1980.4.c.f	16
		1980.4.c.g	16
1980.4.d	\(\chi_{1980}(1781, \cdot)\)	1980.4.d.a	48	1
1980.4.f	\(\chi_{1980}(1871, \cdot)\)	n/a	240	1
1980.4.i	\(\chi_{1980}(1099, \cdot)\)	n/a	536	1
1980.4.k	\(\chi_{1980}(1891, \cdot)\)	n/a	360	1
1980.4.l	\(\chi_{1980}(1079, \cdot)\)	n/a	360	1
1980.4.n	\(\chi_{1980}(989, \cdot)\)	1980.4.n.a	72	1
1980.4.q	\(\chi_{1980}(661, \cdot)\)	n/a	240	2
1980.4.r	\(\chi_{1980}(1187, \cdot)\)	n/a	864	2
1980.4.u	\(\chi_{1980}(1277, \cdot)\)	n/a	120	2
1980.4.v	\(\chi_{1980}(1387, \cdot)\)	n/a	900	2
1980.4.y	\(\chi_{1980}(1297, \cdot)\)	n/a	180	2
1980.4.z	\(\chi_{1980}(181, \cdot)\)	n/a	240	4
1980.4.ba	\(\chi_{1980}(329, \cdot)\)	n/a	432	2
1980.4.be	\(\chi_{1980}(571, \cdot)\)	n/a	1728	2
1980.4.bf	\(\chi_{1980}(419, \cdot)\)	n/a	2160	2
1980.4.bh	\(\chi_{1980}(551, \cdot)\)	n/a	1440	2
1980.4.bk	\(\chi_{1980}(439, \cdot)\)	n/a	2576	2
1980.4.bm	\(\chi_{1980}(529, \cdot)\)	n/a	360	2
1980.4.bn	\(\chi_{1980}(461, \cdot)\)	n/a	288	2
1980.4.br	\(\chi_{1980}(629, \cdot)\)	n/a	288	4
1980.4.bt	\(\chi_{1980}(179, \cdot)\)	n/a	1728	4
1980.4.bu	\(\chi_{1980}(271, \cdot)\)	n/a	1440	4
1980.4.bw	\(\chi_{1980}(19, \cdot)\)	n/a	2144	4
1980.4.bz	\(\chi_{1980}(71, \cdot)\)	n/a	1152	4
1980.4.cb	\(\chi_{1980}(161, \cdot)\)	n/a	192	4
1980.4.cc	\(\chi_{1980}(289, \cdot)\)	n/a	360	4
1980.4.ce	\(\chi_{1980}(353, \cdot)\)	n/a	720	4
1980.4.ch	\(\chi_{1980}(263, \cdot)\)	n/a	5152	4
1980.4.ci	\(\chi_{1980}(373, \cdot)\)	n/a	864	4
1980.4.cl	\(\chi_{1980}(67, \cdot)\)	n/a	4320	4
1980.4.cm	\(\chi_{1980}(301, \cdot)\)	n/a	1152	8
1980.4.cn	\(\chi_{1980}(73, \cdot)\)	n/a	720	8
1980.4.cq	\(\chi_{1980}(163, \cdot)\)	n/a	4288	8
1980.4.cr	\(\chi_{1980}(53, \cdot)\)	n/a	576	8
1980.4.cu	\(\chi_{1980}(107, \cdot)\)	n/a	3456	8
1980.4.cw	\(\chi_{1980}(41, \cdot)\)	n/a	1152	8
1980.4.cx	\(\chi_{1980}(49, \cdot)\)	n/a	1728	8
1980.4.cz	\(\chi_{1980}(79, \cdot)\)	n/a	10304	8
1980.4.dc	\(\chi_{1980}(191, \cdot)\)	n/a	6912	8
1980.4.de	\(\chi_{1980}(59, \cdot)\)	n/a	10304	8
1980.4.df	\(\chi_{1980}(151, \cdot)\)	n/a	6912	8
1980.4.dj	\(\chi_{1980}(29, \cdot)\)	n/a	1728	8
1980.4.dk	\(\chi_{1980}(103, \cdot)\)	n/a	20608	16
1980.4.dn	\(\chi_{1980}(13, \cdot)\)	n/a	3456	16
1980.4.do	\(\chi_{1980}(83, \cdot)\)	n/a	20608	16
1980.4.dr	\(\chi_{1980}(113, \cdot)\)	n/a	3456	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1980))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1980)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(990))\)\(^{\oplus 2}\)