Space of modular forms of level 810 and weight 4

• Label: 810.4
• Level: 810
• Weight: 4
• Dimension: 12672
• Nonzero newspaces: 12
• Sturm bound: 139968
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(139968\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(810))\).

	Total	New	Old
Modular forms	53352	12672	40680
Cusp forms	51624	12672	38952
Eisenstein series	1728	0	1728

Trace form

12672 * q - 24 * q^5 + 72 * q^7 + 48 * q^8 + 36 * q^10 - 102 * q^11 - 180 * q^13 - 264 * q^14 + 408 * q^17 + 828 * q^18 + 1620 * q^19 + 480 * q^20 + 432 * q^21 - 252 * q^22 - 2832 * q^23 - 1242 * q^25 - 4680 * q^26 - 2808 * q^27 - 1152 * q^28 - 3684 * q^29 - 756 * q^30 - 324 * q^31 + 1728 * q^33 + 2052 * q^34 + 7044 * q^35 + 2304 * q^36 + 4716 * q^37 + 3108 * q^38 - 432 * q^40 + 4674 * q^41 + 126 * q^43 - 528 * q^44 + 1026 * q^45 - 1008 * q^46 - 5424 * q^47 - 5364 * q^49 - 2136 * q^50 - 5922 * q^51 - 432 * q^52 - 9540 * q^53 - 1152 * q^55 + 1056 * q^56 - 4428 * q^57 + 3168 * q^58 + 162 * q^59 + 1944 * q^61 + 2976 * q^62 + 3996 * q^63 - 1152 * q^64 + 2130 * q^65 - 18720 * q^66 + 15498 * q^67 - 672 * q^68 - 8244 * q^69 + 1368 * q^70 - 2400 * q^71 + 1152 * q^72 + 1008 * q^73 + 4776 * q^74 - 3960 * q^76 + 24984 * q^77 + 21312 * q^78 - 14868 * q^79 + 1920 * q^80 + 23040 * q^81 - 2088 * q^82 + 6276 * q^83 + 4896 * q^84 - 11448 * q^85 + 7164 * q^86 + 21888 * q^87 - 1008 * q^88 + 1632 * q^89 - 1440 * q^90 + 5400 * q^91 - 2976 * q^92 - 18180 * q^93 + 12312 * q^94 - 9252 * q^95 - 5760 * q^96 + 16506 * q^97 - 21828 * q^98 - 41508 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(810))\)

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
810.4.a	\(\chi_{810}(1, \cdot)\)	810.4.a.a	1	1
		810.4.a.b	1
		810.4.a.c	1
		810.4.a.d	1
		810.4.a.e	1
		810.4.a.f	1
		810.4.a.g	2
		810.4.a.h	2
		810.4.a.i	2
		810.4.a.j	2
		810.4.a.k	2
		810.4.a.l	2
		810.4.a.m	2
		810.4.a.n	2
		810.4.a.o	2
		810.4.a.p	2
		810.4.a.q	3
		810.4.a.r	3
		810.4.a.s	4
		810.4.a.t	4
		810.4.a.u	4
		810.4.a.v	4
810.4.c	\(\chi_{810}(649, \cdot)\)	810.4.c.a	10	1
		810.4.c.b	10
		810.4.c.c	16
		810.4.c.d	18
		810.4.c.e	18
810.4.e	\(\chi_{810}(271, \cdot)\)	810.4.e.a	2	2
		810.4.e.b	2
		810.4.e.c	2
		810.4.e.d	2
		810.4.e.e	2
		810.4.e.f	2
		810.4.e.g	2
		810.4.e.h	2
		810.4.e.i	2
		810.4.e.j	2
		810.4.e.k	2
		810.4.e.l	2
		810.4.e.m	2
		810.4.e.n	2
		810.4.e.o	2
		810.4.e.p	2
		810.4.e.q	2
		810.4.e.r	2
		810.4.e.s	2
		810.4.e.t	2
		810.4.e.u	2
		810.4.e.v	2
		810.4.e.w	2
		810.4.e.x	2
		810.4.e.y	4
		810.4.e.z	4
		810.4.e.ba	4
		810.4.e.bb	4
		810.4.e.bc	4
		810.4.e.bd	4
		810.4.e.be	4
		810.4.e.bf	4
		810.4.e.bg	8
		810.4.e.bh	8
810.4.f	\(\chi_{810}(323, \cdot)\)	n/a	144	2
810.4.i	\(\chi_{810}(109, \cdot)\)	n/a	144	2
810.4.k	\(\chi_{810}(91, \cdot)\)	n/a	216	6
810.4.m	\(\chi_{810}(53, \cdot)\)	n/a	288	4
810.4.p	\(\chi_{810}(19, \cdot)\)	n/a	324	6
810.4.q	\(\chi_{810}(31, \cdot)\)	n/a	1944	18
810.4.s	\(\chi_{810}(17, \cdot)\)	n/a	648	12
810.4.v	\(\chi_{810}(49, \cdot)\)	n/a	2916	18
810.4.w	\(\chi_{810}(23, \cdot)\)	n/a	5832	36

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(810))\) into lower level spaces

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