Space of modular forms of level 504 and weight 3

• Label: 504.3
• Level: 504
• Weight: 3
• Dimension: 5810
• Nonzero newspaces: 30
• Sturm bound: 41472
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 30 \)
Sturm bound:			\(41472\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(504))\).

	Total	New	Old
Modular forms	14400	5990	8410
Cusp forms	13248	5810	7438
Eisenstein series	1152	180	972

Trace form

5810 * q - 10 * q^2 - 12 * q^3 - 22 * q^4 - 32 * q^6 - 40 * q^7 - 88 * q^8 - 60 * q^9 - 70 * q^10 - 74 * q^11 + 4 * q^12 + 32 * q^13 + 60 * q^14 - 60 * q^15 + 226 * q^16 - 56 * q^17 + 168 * q^18 - 142 * q^19 + 156 * q^20 + 36 * q^21 - 110 * q^22 + 66 * q^23 + 24 * q^24 - 74 * q^25 - 96 * q^26 + 336 * q^27 - 174 * q^28 + 216 * q^29 + 124 * q^30 + 126 * q^31 - 40 * q^32 - 196 * q^33 + 30 * q^34 + 6 * q^35 - 52 * q^36 - 204 * q^37 + 400 * q^38 - 108 * q^39 + 784 * q^40 - 380 * q^41 - 218 * q^42 + 192 * q^43 - 14 * q^44 - 328 * q^45 + 296 * q^46 - 618 * q^47 - 688 * q^48 - 254 * q^49 - 886 * q^50 - 84 * q^51 - 604 * q^52 + 396 * q^53 - 552 * q^54 - 520 * q^55 - 684 * q^56 + 484 * q^57 - 708 * q^58 + 418 * q^59 - 1128 * q^60 + 404 * q^61 - 756 * q^62 + 466 * q^63 + 386 * q^64 + 1488 * q^65 + 64 * q^66 + 938 * q^67 + 982 * q^68 + 712 * q^69 + 1552 * q^70 + 1428 * q^71 + 1584 * q^72 + 684 * q^73 + 2238 * q^74 - 68 * q^75 + 1130 * q^76 + 1684 * q^78 + 738 * q^79 + 2256 * q^80 - 772 * q^81 + 146 * q^82 - 200 * q^83 + 712 * q^84 + 256 * q^85 + 1006 * q^86 - 732 * q^87 + 154 * q^88 - 164 * q^89 + 880 * q^90 + 84 * q^91 + 6 * q^92 - 16 * q^93 - 126 * q^94 + 30 * q^95 - 432 * q^96 - 540 * q^97 - 1462 * q^98 - 180 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(504))\)

We only show spaces with odd 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
504.3.d	\(\chi_{504}(449, \cdot)\)	504.3.d.a	4	1
		504.3.d.b	8
504.3.e	\(\chi_{504}(251, \cdot)\)	504.3.e.a	8	1
		504.3.e.b	8
		504.3.e.c	48
504.3.f	\(\chi_{504}(433, \cdot)\)	504.3.f.a	4	1
		504.3.f.b	8
		504.3.f.c	8
504.3.g	\(\chi_{504}(379, \cdot)\)	504.3.g.a	4	1
		504.3.g.b	8
		504.3.g.c	24
		504.3.g.d	24
504.3.l	\(\chi_{504}(181, \cdot)\)	504.3.l.a	2	1
		504.3.l.b	2
		504.3.l.c	2
		504.3.l.d	4
		504.3.l.e	4
		504.3.l.f	8
		504.3.l.g	24
		504.3.l.h	32
504.3.m	\(\chi_{504}(127, \cdot)\)	None	0	1
504.3.n	\(\chi_{504}(197, \cdot)\)	504.3.n.a	48	1
504.3.o	\(\chi_{504}(503, \cdot)\)	None	0	1
504.3.u	\(\chi_{504}(59, \cdot)\)	n/a	376	2
504.3.v	\(\chi_{504}(65, \cdot)\)	504.3.v.a	96	2
504.3.ba	\(\chi_{504}(67, \cdot)\)	n/a	376	2
504.3.bb	\(\chi_{504}(313, \cdot)\)	504.3.bb.a	96	2
504.3.bc	\(\chi_{504}(143, \cdot)\)	None	0	2
504.3.bd	\(\chi_{504}(53, \cdot)\)	n/a	128	2
504.3.bg	\(\chi_{504}(29, \cdot)\)	n/a	288	2
504.3.bh	\(\chi_{504}(383, \cdot)\)	None	0	2
504.3.bi	\(\chi_{504}(149, \cdot)\)	n/a	376	2
504.3.bj	\(\chi_{504}(167, \cdot)\)	None	0	2
504.3.bn	\(\chi_{504}(13, \cdot)\)	n/a	376	2
504.3.bo	\(\chi_{504}(151, \cdot)\)	None	0	2
504.3.bp	\(\chi_{504}(229, \cdot)\)	n/a	376	2
504.3.bq	\(\chi_{504}(295, \cdot)\)	None	0	2
504.3.bv	\(\chi_{504}(415, \cdot)\)	None	0	2
504.3.bw	\(\chi_{504}(325, \cdot)\)	n/a	156	2
504.3.bx	\(\chi_{504}(163, \cdot)\)	n/a	156	2
504.3.by	\(\chi_{504}(73, \cdot)\)	504.3.by.a	8	2
		504.3.by.b	8
		504.3.by.c	8
		504.3.by.d	16
504.3.cd	\(\chi_{504}(97, \cdot)\)	504.3.cd.a	96	2
504.3.ce	\(\chi_{504}(403, \cdot)\)	n/a	376	2
504.3.cf	\(\chi_{504}(241, \cdot)\)	504.3.cf.a	96	2
504.3.cg	\(\chi_{504}(43, \cdot)\)	n/a	288	2
504.3.cl	\(\chi_{504}(113, \cdot)\)	504.3.cl.a	72	2
504.3.cm	\(\chi_{504}(131, \cdot)\)	n/a	376	2
504.3.cn	\(\chi_{504}(137, \cdot)\)	504.3.cn.a	96	2
504.3.co	\(\chi_{504}(83, \cdot)\)	n/a	376	2
504.3.ct	\(\chi_{504}(395, \cdot)\)	n/a	128	2
504.3.cu	\(\chi_{504}(233, \cdot)\)	504.3.cu.a	16	2
		504.3.cu.b	16
504.3.cv	\(\chi_{504}(79, \cdot)\)	None	0	2
504.3.cw	\(\chi_{504}(61, \cdot)\)	n/a	376	2
504.3.da	\(\chi_{504}(47, \cdot)\)	None	0	2
504.3.db	\(\chi_{504}(221, \cdot)\)	n/a	376	2

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(504))\) into lower level spaces

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