Space of modular forms of level 504 and weight 6

• Label: 504.6
• Level: 504
• Weight: 6
• Dimension: 14658
• Nonzero newspaces: 30
• Sturm bound: 82944
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 30 \)
Sturm bound:			\(82944\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(504))\).

	Total	New	Old
Modular forms	35136	14838	20298
Cusp forms	33984	14658	19326
Eisenstein series	1152	180	972

Trace form

14658 * q - 10 * q^2 + 6 * q^3 - 54 * q^4 - 52 * q^5 + 112 * q^6 - 136 * q^7 - 1240 * q^8 + 282 * q^9 + 970 * q^10 + 2162 * q^11 + 2164 * q^12 - 942 * q^13 + 220 * q^14 - 960 * q^15 - 8478 * q^16 - 118 * q^17 + 8952 * q^18 - 3658 * q^19 - 268 * q^20 - 2268 * q^21 - 24846 * q^22 + 19860 * q^23 - 18120 * q^24 + 24400 * q^25 - 7552 * q^26 + 6600 * q^27 + 37586 * q^28 - 25560 * q^29 + 77308 * q^30 + 3664 * q^31 - 35360 * q^32 - 15010 * q^33 - 55426 * q^34 - 79446 * q^35 - 133684 * q^36 + 17610 * q^37 + 58384 * q^38 + 77508 * q^39 + 75928 * q^40 + 20162 * q^41 + 96046 * q^42 + 38282 * q^43 + 49170 * q^44 - 3172 * q^45 + 8304 * q^46 - 246804 * q^47 - 282496 * q^48 - 123786 * q^49 - 266686 * q^50 - 123294 * q^51 - 159852 * q^52 - 25378 * q^53 + 88584 * q^54 + 398528 * q^55 + 120052 * q^56 - 44606 * q^57 + 374860 * q^58 + 424784 * q^59 - 128568 * q^60 + 10476 * q^61 - 152156 * q^62 + 42856 * q^63 + 491346 * q^64 - 93440 * q^65 - 223424 * q^66 - 541414 * q^67 - 863682 * q^68 - 159488 * q^69 - 249848 * q^70 - 345728 * q^71 + 1001520 * q^72 + 73758 * q^73 + 1340990 * q^74 + 230674 * q^75 + 500330 * q^76 + 151302 * q^77 - 640988 * q^78 - 20720 * q^79 - 1307304 * q^80 - 19186 * q^81 + 8210 * q^82 + 83002 * q^83 - 1283336 * q^84 - 537144 * q^85 - 169954 * q^86 + 178728 * q^87 - 25158 * q^88 + 457154 * q^89 - 16112 * q^90 + 389742 * q^91 + 80502 * q^92 + 888716 * q^93 + 631890 * q^94 + 306800 * q^95 + 1757088 * q^96 - 516798 * q^97 + 1291010 * q^98 - 113364 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(504))\)

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
504.6.a	\(\chi_{504}(1, \cdot)\)	504.6.a.a	1	1
		504.6.a.b	1
		504.6.a.c	1
		504.6.a.d	1
		504.6.a.e	1
		504.6.a.f	1
		504.6.a.g	1
		504.6.a.h	1
		504.6.a.i	2
		504.6.a.j	2
		504.6.a.k	2
		504.6.a.l	2
		504.6.a.m	2
		504.6.a.n	2
		504.6.a.o	2
		504.6.a.p	2
		504.6.a.q	2
		504.6.a.r	2
		504.6.a.s	2
		504.6.a.t	2
		504.6.a.u	2
		504.6.a.v	2
		504.6.a.w	2
504.6.b	\(\chi_{504}(55, \cdot)\)	None	0	1
504.6.c	\(\chi_{504}(253, \cdot)\)	n/a	150	1
504.6.h	\(\chi_{504}(71, \cdot)\)	None	0	1
504.6.i	\(\chi_{504}(125, \cdot)\)	n/a	160	1
504.6.j	\(\chi_{504}(323, \cdot)\)	n/a	120	1
504.6.k	\(\chi_{504}(377, \cdot)\)	504.6.k.a	40	1
504.6.p	\(\chi_{504}(307, \cdot)\)	n/a	198	1
504.6.q	\(\chi_{504}(25, \cdot)\)	n/a	240	2
504.6.r	\(\chi_{504}(169, \cdot)\)	n/a	180	2
504.6.s	\(\chi_{504}(289, \cdot)\)	504.6.s.a	8	2
		504.6.s.b	10
		504.6.s.c	10
		504.6.s.d	10
		504.6.s.e	10
		504.6.s.f	12
		504.6.s.g	20
		504.6.s.h	20
504.6.t	\(\chi_{504}(193, \cdot)\)	n/a	240	2
504.6.w	\(\chi_{504}(205, \cdot)\)	n/a	952	2
504.6.x	\(\chi_{504}(31, \cdot)\)	None	0	2
504.6.y	\(\chi_{504}(173, \cdot)\)	n/a	952	2
504.6.z	\(\chi_{504}(95, \cdot)\)	None	0	2
504.6.be	\(\chi_{504}(139, \cdot)\)	n/a	952	2
504.6.bf	\(\chi_{504}(115, \cdot)\)	n/a	952	2
504.6.bk	\(\chi_{504}(19, \cdot)\)	n/a	396	2
504.6.bl	\(\chi_{504}(17, \cdot)\)	504.6.bl.a	80	2
504.6.bm	\(\chi_{504}(107, \cdot)\)	n/a	320	2
504.6.br	\(\chi_{504}(155, \cdot)\)	n/a	720	2
504.6.bs	\(\chi_{504}(257, \cdot)\)	n/a	240	2
504.6.bt	\(\chi_{504}(11, \cdot)\)	n/a	952	2
504.6.bu	\(\chi_{504}(41, \cdot)\)	n/a	240	2
504.6.bz	\(\chi_{504}(239, \cdot)\)	None	0	2
504.6.ca	\(\chi_{504}(5, \cdot)\)	n/a	952	2
504.6.cb	\(\chi_{504}(23, \cdot)\)	None	0	2
504.6.cc	\(\chi_{504}(293, \cdot)\)	n/a	952	2
504.6.ch	\(\chi_{504}(269, \cdot)\)	n/a	320	2
504.6.ci	\(\chi_{504}(359, \cdot)\)	None	0	2
504.6.cj	\(\chi_{504}(37, \cdot)\)	n/a	396	2
504.6.ck	\(\chi_{504}(199, \cdot)\)	None	0	2
504.6.cp	\(\chi_{504}(223, \cdot)\)	None	0	2
504.6.cq	\(\chi_{504}(277, \cdot)\)	n/a	952	2
504.6.cr	\(\chi_{504}(103, \cdot)\)	None	0	2
504.6.cs	\(\chi_{504}(85, \cdot)\)	n/a	720	2
504.6.cx	\(\chi_{504}(185, \cdot)\)	n/a	240	2
504.6.cy	\(\chi_{504}(347, \cdot)\)	n/a	952	2
504.6.cz	\(\chi_{504}(187, \cdot)\)	n/a	952	2

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(504))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(504)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 2}\)