Space of modular forms of level 816 and weight 4

• Label: 816.4
• Level: 816
• Weight: 4
• Dimension: 23030
• Nonzero newspaces: 26
• Sturm bound: 147456
• Trace bound: 19

Defining parameters

Level:	\( N \)	=	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 26 \)
Sturm bound:			\(147456\)
Trace bound:			\(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(816))\).

	Total	New	Old
Modular forms	56192	23302	32890
Cusp forms	54400	23030	31370
Eisenstein series	1792	272	1520

Trace form

23030 * q - 14 * q^3 - 16 * q^4 - 4 * q^5 - 88 * q^6 - 96 * q^7 - 168 * q^8 - 122 * q^9 - 320 * q^10 + 120 * q^11 + 176 * q^12 - 52 * q^13 + 696 * q^14 - 324 * q^15 + 544 * q^16 + 26 * q^17 - 96 * q^18 - 112 * q^19 - 160 * q^20 + 480 * q^21 - 1392 * q^22 + 496 * q^23 - 248 * q^24 + 426 * q^25 + 40 * q^26 + 298 * q^27 + 1216 * q^28 - 116 * q^29 + 1448 * q^30 + 1392 * q^31 + 1920 * q^32 - 1184 * q^33 + 120 * q^34 - 240 * q^35 + 960 * q^36 - 2308 * q^37 - 2512 * q^38 - 1948 * q^39 - 4816 * q^40 - 828 * q^41 - 2744 * q^42 - 848 * q^43 + 400 * q^44 + 2732 * q^45 + 1472 * q^46 + 1152 * q^47 - 1376 * q^48 + 2702 * q^49 - 1416 * q^50 + 558 * q^51 - 2784 * q^52 + 2108 * q^53 - 3432 * q^54 + 6000 * q^55 - 2688 * q^56 - 1816 * q^57 - 3088 * q^58 + 1736 * q^59 + 816 * q^60 - 1908 * q^61 + 1992 * q^62 - 6360 * q^63 + 4160 * q^64 - 8504 * q^65 + 4040 * q^66 + 2848 * q^67 + 1568 * q^68 - 8 * q^69 + 13840 * q^70 - 2704 * q^71 + 8600 * q^72 + 4892 * q^73 + 5480 * q^74 - 4570 * q^75 + 4832 * q^76 - 2400 * q^77 + 6448 * q^78 - 5872 * q^79 - 1424 * q^80 + 6558 * q^81 - 1520 * q^82 + 4872 * q^83 + 560 * q^84 + 2396 * q^85 + 3424 * q^86 - 5004 * q^87 - 9920 * q^88 + 132 * q^89 - 6672 * q^90 + 8272 * q^91 - 10592 * q^92 + 6024 * q^93 - 21840 * q^94 + 21872 * q^95 - 21808 * q^96 + 1180 * q^97 - 13520 * q^98 - 1336 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(816))\)

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
816.4.a	\(\chi_{816}(1, \cdot)\)	816.4.a.a	1	1
		816.4.a.b	1
		816.4.a.c	1
		816.4.a.d	1
		816.4.a.e	1
		816.4.a.f	1
		816.4.a.g	1
		816.4.a.h	1
		816.4.a.i	1
		816.4.a.j	1
		816.4.a.k	2
		816.4.a.l	2
		816.4.a.m	2
		816.4.a.n	2
		816.4.a.o	2
		816.4.a.p	2
		816.4.a.q	3
		816.4.a.r	3
		816.4.a.s	3
		816.4.a.t	3
		816.4.a.u	3
		816.4.a.v	3
		816.4.a.w	4
		816.4.a.x	4
816.4.c	\(\chi_{816}(577, \cdot)\)	816.4.c.a	2	1
		816.4.c.b	4
		816.4.c.c	6
		816.4.c.d	6
		816.4.c.e	6
		816.4.c.f	8
		816.4.c.g	10
		816.4.c.h	12
816.4.e	\(\chi_{816}(239, \cdot)\)	816.4.e.a	32	1
		816.4.e.b	64
816.4.f	\(\chi_{816}(409, \cdot)\)	None	0	1
816.4.h	\(\chi_{816}(407, \cdot)\)	None	0	1
816.4.j	\(\chi_{816}(647, \cdot)\)	None	0	1
816.4.l	\(\chi_{816}(169, \cdot)\)	None	0	1
816.4.o	\(\chi_{816}(815, \cdot)\)	n/a	108	1
816.4.r	\(\chi_{816}(395, \cdot)\)	n/a	856	2
816.4.s	\(\chi_{816}(157, \cdot)\)	n/a	432	2
816.4.u	\(\chi_{816}(205, \cdot)\)	n/a	384	2
816.4.w	\(\chi_{816}(203, \cdot)\)	n/a	856	2
816.4.y	\(\chi_{816}(455, \cdot)\)	None	0	2
816.4.ba	\(\chi_{816}(217, \cdot)\)	None	0	2
816.4.bd	\(\chi_{816}(625, \cdot)\)	n/a	108	2
816.4.bf	\(\chi_{816}(47, \cdot)\)	n/a	216	2
816.4.bh	\(\chi_{816}(35, \cdot)\)	n/a	768	2
816.4.bj	\(\chi_{816}(373, \cdot)\)	n/a	432	2
816.4.bl	\(\chi_{816}(13, \cdot)\)	n/a	432	2
816.4.bm	\(\chi_{816}(251, \cdot)\)	n/a	856	2
816.4.bq	\(\chi_{816}(49, \cdot)\)	n/a	216	4
816.4.br	\(\chi_{816}(287, \cdot)\)	n/a	432	4
816.4.bs	\(\chi_{816}(155, \cdot)\)	n/a	1712	4
816.4.bt	\(\chi_{816}(229, \cdot)\)	n/a	864	4
816.4.bw	\(\chi_{816}(59, \cdot)\)	n/a	1712	4
816.4.bx	\(\chi_{816}(325, \cdot)\)	n/a	864	4
816.4.ca	\(\chi_{816}(25, \cdot)\)	None	0	4
816.4.cb	\(\chi_{816}(263, \cdot)\)	None	0	4
816.4.cf	\(\chi_{816}(29, \cdot)\)	n/a	3424	8
816.4.cg	\(\chi_{816}(91, \cdot)\)	n/a	1728	8
816.4.cj	\(\chi_{816}(65, \cdot)\)	n/a	848	8
816.4.ck	\(\chi_{816}(31, \cdot)\)	n/a	432	8
816.4.cn	\(\chi_{816}(7, \cdot)\)	None	0	8
816.4.co	\(\chi_{816}(41, \cdot)\)	None	0	8
816.4.cr	\(\chi_{816}(5, \cdot)\)	n/a	3424	8
816.4.cs	\(\chi_{816}(139, \cdot)\)	n/a	1728	8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(816))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(816)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(408))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(816))\)\(^{\oplus 1}\)