Space of modular forms of level 1620 and weight 4

• Label: 1620.4
• Level: 1620
• Weight: 4
• Dimension: 88368
• Nonzero newspaces: 24
• Sturm bound: 559872
• Trace bound: 16

Defining parameters

Level:	\( N \)	=	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(559872\)
Trace bound:			\(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1620))\).

	Total	New	Old
Modular forms	212112	89040	123072
Cusp forms	207792	88368	119424
Eisenstein series	4320	672	3648

Trace form

88368 * q - 24 * q^2 - 40 * q^4 - 60 * q^5 - 108 * q^6 - 36 * q^7 - 30 * q^8 - 72 * q^9 - 103 * q^10 - 174 * q^11 - 36 * q^12 - 44 * q^13 + 126 * q^14 + 240 * q^16 + 348 * q^17 - 36 * q^18 - 540 * q^19 + 195 * q^20 - 432 * q^21 - 80 * q^22 + 948 * q^23 - 36 * q^24 + 150 * q^25 - 42 * q^26 + 1404 * q^27 + 190 * q^28 + 1500 * q^29 - 54 * q^30 + 432 * q^31 - 1404 * q^32 - 936 * q^33 - 1116 * q^34 - 2892 * q^35 - 108 * q^36 - 1088 * q^37 - 1812 * q^38 + 545 * q^40 + 7134 * q^41 + 7074 * q^42 + 3150 * q^43 + 10638 * q^44 + 918 * q^45 + 2090 * q^46 - 2004 * q^47 - 4590 * q^48 - 2928 * q^49 - 8031 * q^50 - 5922 * q^51 - 6210 * q^52 - 9528 * q^53 - 13392 * q^54 - 4932 * q^55 - 17754 * q^56 - 4500 * q^57 - 1502 * q^58 - 7326 * q^59 - 1341 * q^60 - 600 * q^61 + 7494 * q^62 + 3996 * q^63 + 7610 * q^64 + 9354 * q^65 + 14724 * q^66 + 378 * q^67 + 19308 * q^68 + 14148 * q^69 + 551 * q^70 + 1200 * q^71 - 36 * q^72 + 2260 * q^73 + 906 * q^74 + 452 * q^76 - 8208 * q^77 - 522 * q^78 + 8568 * q^79 + 132 * q^80 - 11736 * q^81 - 1116 * q^82 - 7368 * q^83 + 450 * q^84 + 2098 * q^85 - 48 * q^86 - 10944 * q^87 - 8648 * q^88 + 14916 * q^89 - 12591 * q^90 + 2916 * q^91 - 49386 * q^92 + 36828 * q^93 - 14426 * q^94 + 3276 * q^95 - 5958 * q^96 - 9674 * q^97 + 7722 * q^98 + 15084 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1620))\)

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
1620.4.a	\(\chi_{1620}(1, \cdot)\)	1620.4.a.a	1	1
		1620.4.a.b	1
		1620.4.a.c	3
		1620.4.a.d	3
		1620.4.a.e	3
		1620.4.a.f	3
		1620.4.a.g	4
		1620.4.a.h	4
		1620.4.a.i	6
		1620.4.a.j	6
		1620.4.a.k	7
		1620.4.a.l	7
1620.4.d	\(\chi_{1620}(649, \cdot)\)	1620.4.d.a	10	1
		1620.4.d.b	10
		1620.4.d.c	16
		1620.4.d.d	18
		1620.4.d.e	18
1620.4.e	\(\chi_{1620}(971, \cdot)\)	n/a	288	1
1620.4.h	\(\chi_{1620}(1619, \cdot)\)	n/a	424	1
1620.4.i	\(\chi_{1620}(541, \cdot)\)	1620.4.i.a	2	2
		1620.4.i.b	2
		1620.4.i.c	2
		1620.4.i.d	2
		1620.4.i.e	2
		1620.4.i.f	2
		1620.4.i.g	2
		1620.4.i.h	2
		1620.4.i.i	2
		1620.4.i.j	2
		1620.4.i.k	2
		1620.4.i.l	2
		1620.4.i.m	4
		1620.4.i.n	4
		1620.4.i.o	4
		1620.4.i.p	4
		1620.4.i.q	4
		1620.4.i.r	4
		1620.4.i.s	6
		1620.4.i.t	6
		1620.4.i.u	6
		1620.4.i.v	6
		1620.4.i.w	12
		1620.4.i.x	12
1620.4.j	\(\chi_{1620}(1133, \cdot)\)	n/a	144	2
1620.4.k	\(\chi_{1620}(163, \cdot)\)	n/a	848	2
1620.4.n	\(\chi_{1620}(539, \cdot)\)	n/a	856	2
1620.4.q	\(\chi_{1620}(431, \cdot)\)	n/a	576	2
1620.4.r	\(\chi_{1620}(109, \cdot)\)	n/a	144	2
1620.4.u	\(\chi_{1620}(181, \cdot)\)	n/a	216	6
1620.4.x	\(\chi_{1620}(53, \cdot)\)	n/a	288	4
1620.4.y	\(\chi_{1620}(703, \cdot)\)	n/a	1712	4
1620.4.bb	\(\chi_{1620}(179, \cdot)\)	n/a	1920	6
1620.4.bd	\(\chi_{1620}(289, \cdot)\)	n/a	324	6
1620.4.be	\(\chi_{1620}(71, \cdot)\)	n/a	1296	6
1620.4.bg	\(\chi_{1620}(61, \cdot)\)	n/a	1944	18
1620.4.bi	\(\chi_{1620}(127, \cdot)\)	n/a	3840	12
1620.4.bk	\(\chi_{1620}(17, \cdot)\)	n/a	648	12
1620.4.bm	\(\chi_{1620}(59, \cdot)\)	n/a	17424	18
1620.4.bo	\(\chi_{1620}(11, \cdot)\)	n/a	11664	18
1620.4.br	\(\chi_{1620}(49, \cdot)\)	n/a	2916	18
1620.4.bs	\(\chi_{1620}(77, \cdot)\)	n/a	5832	36
1620.4.bv	\(\chi_{1620}(7, \cdot)\)	n/a	34848	36

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1620))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1620)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(810))\)\(^{\oplus 2}\)