Space of modular forms of level 585 and weight 6

• Label: 585.6
• Level: 585
• Weight: 6
• Dimension: 43068
• Nonzero newspaces: 50
• Sturm bound: 145152
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 50 \)
Sturm bound:			\(145152\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(585))\).

	Total	New	Old
Modular forms	61248	43664	17584
Cusp forms	59712	43068	16644
Eisenstein series	1536	596	940

Trace form

43068 * q + 4 * q^2 - 80 * q^3 - 104 * q^4 + 228 * q^5 + 572 * q^6 + 136 * q^7 - 5124 * q^8 - 1936 * q^9 + 4606 * q^10 + 7336 * q^11 + 10352 * q^12 + 1642 * q^13 - 9312 * q^14 - 8504 * q^15 - 17408 * q^16 - 10958 * q^17 - 23600 * q^18 + 4340 * q^19 + 20330 * q^20 + 30408 * q^21 + 27348 * q^22 + 57372 * q^23 + 26748 * q^24 + 24690 * q^25 - 11956 * q^26 - 60896 * q^27 - 194128 * q^28 - 51130 * q^29 + 15944 * q^30 + 35400 * q^31 + 156476 * q^32 + 90968 * q^33 + 96368 * q^34 + 30284 * q^35 - 271268 * q^36 + 45194 * q^37 - 302468 * q^38 - 146776 * q^39 - 221308 * q^40 - 197950 * q^41 + 138960 * q^42 - 123224 * q^43 + 642944 * q^44 + 343640 * q^45 + 161588 * q^46 + 266752 * q^47 + 137756 * q^48 + 347422 * q^49 + 7348 * q^50 - 253936 * q^51 - 44216 * q^52 + 220276 * q^53 - 229636 * q^54 + 236760 * q^55 - 464376 * q^56 - 525272 * q^57 - 978828 * q^58 - 731888 * q^59 - 362596 * q^60 - 625494 * q^61 - 1075212 * q^62 + 76392 * q^63 + 353760 * q^64 + 451631 * q^65 + 1521352 * q^66 + 1466812 * q^67 + 3144188 * q^68 + 591648 * q^69 + 1524444 * q^70 + 150332 * q^71 + 273540 * q^72 - 526424 * q^73 - 2640172 * q^74 - 1316720 * q^75 - 3396608 * q^76 - 2777304 * q^77 - 3229580 * q^78 - 978552 * q^79 - 3134524 * q^80 - 175192 * q^81 - 916860 * q^82 + 973368 * q^83 + 2536008 * q^84 + 1294159 * q^85 + 5917372 * q^86 + 2054008 * q^87 + 4007772 * q^88 + 1462344 * q^89 + 2893036 * q^90 + 193648 * q^91 + 3159840 * q^92 + 1188960 * q^93 - 803188 * q^94 - 387578 * q^95 - 1086680 * q^96 + 388016 * q^97 + 535616 * q^98 - 1035128 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(585))\)

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
585.6.a	\(\chi_{585}(1, \cdot)\)	585.6.a.a	1	1
		585.6.a.b	1
		585.6.a.c	3
		585.6.a.d	4
		585.6.a.e	4
		585.6.a.f	4
		585.6.a.g	4
		585.6.a.h	4
		585.6.a.i	5
		585.6.a.j	5
		585.6.a.k	6
		585.6.a.l	6
		585.6.a.m	6
		585.6.a.n	7
		585.6.a.o	9
		585.6.a.p	9
		585.6.a.q	11
		585.6.a.r	11
585.6.b	\(\chi_{585}(181, \cdot)\)	n/a	118	1
585.6.c	\(\chi_{585}(469, \cdot)\)	n/a	150	1
585.6.h	\(\chi_{585}(64, \cdot)\)	n/a	172	1
585.6.i	\(\chi_{585}(196, \cdot)\)	n/a	480	2
585.6.j	\(\chi_{585}(406, \cdot)\)	n/a	232	2
585.6.k	\(\chi_{585}(61, \cdot)\)	n/a	560	2
585.6.l	\(\chi_{585}(16, \cdot)\)	n/a	560	2
585.6.n	\(\chi_{585}(307, \cdot)\)	n/a	346	2
585.6.p	\(\chi_{585}(53, \cdot)\)	n/a	240	2
585.6.q	\(\chi_{585}(44, \cdot)\)	n/a	280	2
585.6.r	\(\chi_{585}(161, \cdot)\)	n/a	192	2
585.6.v	\(\chi_{585}(233, \cdot)\)	n/a	280	2
585.6.w	\(\chi_{585}(73, \cdot)\)	n/a	346	2
585.6.ba	\(\chi_{585}(121, \cdot)\)	n/a	560	2
585.6.bb	\(\chi_{585}(139, \cdot)\)	n/a	832	2
585.6.be	\(\chi_{585}(259, \cdot)\)	n/a	832	2
585.6.bf	\(\chi_{585}(199, \cdot)\)	n/a	344	2
585.6.bk	\(\chi_{585}(49, \cdot)\)	n/a	832	2
585.6.bl	\(\chi_{585}(94, \cdot)\)	n/a	832	2
585.6.bm	\(\chi_{585}(166, \cdot)\)	n/a	560	2
585.6.br	\(\chi_{585}(79, \cdot)\)	n/a	720	2
585.6.bs	\(\chi_{585}(289, \cdot)\)	n/a	348	2
585.6.bt	\(\chi_{585}(376, \cdot)\)	n/a	560	2
585.6.bu	\(\chi_{585}(316, \cdot)\)	n/a	232	2
585.6.bx	\(\chi_{585}(4, \cdot)\)	n/a	832	2
585.6.ca	\(\chi_{585}(58, \cdot)\)	n/a	1664	4
585.6.cc	\(\chi_{585}(67, \cdot)\)	n/a	1664	4
585.6.cf	\(\chi_{585}(163, \cdot)\)	n/a	692	4
585.6.cg	\(\chi_{585}(187, \cdot)\)	n/a	1664	4
585.6.ci	\(\chi_{585}(113, \cdot)\)	n/a	1664	4
585.6.cm	\(\chi_{585}(11, \cdot)\)	n/a	1120	4
585.6.cn	\(\chi_{585}(59, \cdot)\)	n/a	1664	4
585.6.co	\(\chi_{585}(212, \cdot)\)	n/a	1664	4
585.6.cr	\(\chi_{585}(23, \cdot)\)	n/a	1664	4
585.6.cs	\(\chi_{585}(38, \cdot)\)	n/a	1664	4
585.6.cv	\(\chi_{585}(17, \cdot)\)	n/a	560	4
585.6.cw	\(\chi_{585}(71, \cdot)\)	n/a	368	4
585.6.cx	\(\chi_{585}(89, \cdot)\)	n/a	560	4
585.6.dc	\(\chi_{585}(164, \cdot)\)	n/a	1664	4
585.6.dd	\(\chi_{585}(41, \cdot)\)	n/a	1120	4
585.6.de	\(\chi_{585}(254, \cdot)\)	n/a	1664	4
585.6.df	\(\chi_{585}(86, \cdot)\)	n/a	1120	4
585.6.dj	\(\chi_{585}(92, \cdot)\)	n/a	1440	4
585.6.dk	\(\chi_{585}(68, \cdot)\)	n/a	1664	4
585.6.dn	\(\chi_{585}(107, \cdot)\)	n/a	560	4
585.6.dp	\(\chi_{585}(28, \cdot)\)	n/a	692	4
585.6.dq	\(\chi_{585}(112, \cdot)\)	n/a	1664	4
585.6.dt	\(\chi_{585}(7, \cdot)\)	n/a	1664	4
585.6.dv	\(\chi_{585}(292, \cdot)\)	n/a	1664	4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(585))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(585)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(585))\)\(^{\oplus 1}\)