Space of modular forms of level 624 and weight 4

• Label: 624.4
• Level: 624
• Weight: 4
• Dimension: 13346
• Nonzero newspaces: 28
• Sturm bound: 86016
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(86016\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(624))\).

	Total	New	Old
Modular forms	32928	13546	19382
Cusp forms	31584	13346	18238
Eisenstein series	1344	200	1144

Trace form

13346 * q - 8 * q^3 - 4 * q^5 - 80 * q^6 - 84 * q^7 - 168 * q^8 - 120 * q^9 - 304 * q^10 + 120 * q^11 + 184 * q^12 - 46 * q^13 + 696 * q^14 - 318 * q^15 + 560 * q^16 + 52 * q^17 - 56 * q^18 - 100 * q^19 - 160 * q^20 + 490 * q^21 - 1376 * q^22 + 496 * q^23 - 240 * q^24 + 442 * q^25 + 20 * q^26 + 286 * q^27 + 1232 * q^28 - 116 * q^29 + 1456 * q^30 + 1404 * q^31 + 1920 * q^32 - 1174 * q^33 + 320 * q^34 - 240 * q^35 + 968 * q^36 - 2288 * q^37 - 2512 * q^38 + 280 * q^39 - 4848 * q^40 + 2004 * q^41 - 2736 * q^42 + 1180 * q^43 + 400 * q^44 + 2526 * q^45 + 1488 * q^46 - 1080 * q^47 - 1368 * q^48 - 1582 * q^49 - 1416 * q^50 - 2532 * q^51 - 1376 * q^52 - 7172 * q^53 - 3424 * q^54 - 8148 * q^55 - 2688 * q^56 - 5574 * q^57 - 3072 * q^58 + 1616 * q^59 + 824 * q^60 + 5992 * q^61 + 1992 * q^62 + 1386 * q^63 + 4176 * q^64 + 5940 * q^65 + 4024 * q^66 + 13844 * q^67 + 3136 * q^68 + 8362 * q^69 + 13856 * q^70 + 2576 * q^71 + 8608 * q^72 + 9632 * q^73 + 5480 * q^74 - 3142 * q^75 + 4848 * q^76 - 5344 * q^77 + 3216 * q^78 - 12136 * q^79 - 1424 * q^80 - 784 * q^81 - 1504 * q^82 - 11736 * q^83 - 7664 * q^84 - 21876 * q^85 - 35552 * q^86 - 11082 * q^87 - 42784 * q^88 - 20412 * q^89 - 31312 * q^90 - 964 * q^91 - 18944 * q^92 + 4690 * q^93 - 16832 * q^94 + 25592 * q^95 - 1496 * q^96 + 12928 * q^97 + 18016 * q^98 + 6638 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(624))\)

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
624.4.a	\(\chi_{624}(1, \cdot)\)	624.4.a.a	1	1
		624.4.a.b	1
		624.4.a.c	1
		624.4.a.d	1
		624.4.a.e	1
		624.4.a.f	1
		624.4.a.g	1
		624.4.a.h	1
		624.4.a.i	1
		624.4.a.j	2
		624.4.a.k	2
		624.4.a.l	2
		624.4.a.m	2
		624.4.a.n	2
		624.4.a.o	2
		624.4.a.p	2
		624.4.a.q	2
		624.4.a.r	2
		624.4.a.s	3
		624.4.a.t	3
		624.4.a.u	3
624.4.c	\(\chi_{624}(337, \cdot)\)	624.4.c.a	2	1
		624.4.c.b	2
		624.4.c.c	4
		624.4.c.d	4
		624.4.c.e	4
		624.4.c.f	4
		624.4.c.g	10
		624.4.c.h	12
624.4.d	\(\chi_{624}(287, \cdot)\)	624.4.d.a	12	1
		624.4.d.b	12
		624.4.d.c	24
		624.4.d.d	24
624.4.g	\(\chi_{624}(313, \cdot)\)	None	0	1
624.4.h	\(\chi_{624}(311, \cdot)\)	None	0	1
624.4.j	\(\chi_{624}(599, \cdot)\)	None	0	1
624.4.m	\(\chi_{624}(25, \cdot)\)	None	0	1
624.4.n	\(\chi_{624}(623, \cdot)\)	624.4.n.a	2	1
		624.4.n.b	2
		624.4.n.c	24
		624.4.n.d	56
624.4.q	\(\chi_{624}(289, \cdot)\)	624.4.q.a	2	2
		624.4.q.b	2
		624.4.q.c	2
		624.4.q.d	4
		624.4.q.e	4
		624.4.q.f	4
		624.4.q.g	6
		624.4.q.h	6
		624.4.q.i	8
		624.4.q.j	8
		624.4.q.k	8
		624.4.q.l	8
		624.4.q.m	10
		624.4.q.n	12
624.4.r	\(\chi_{624}(499, \cdot)\)	n/a	336	2
624.4.u	\(\chi_{624}(5, \cdot)\)	n/a	664	2
624.4.v	\(\chi_{624}(155, \cdot)\)	n/a	664	2
624.4.x	\(\chi_{624}(157, \cdot)\)	n/a	288	2
624.4.bb	\(\chi_{624}(151, \cdot)\)	None	0	2
624.4.bc	\(\chi_{624}(31, \cdot)\)	624.4.bc.a	14	2
		624.4.bc.b	14
		624.4.bc.c	28
		624.4.bc.d	28
624.4.bf	\(\chi_{624}(161, \cdot)\)	n/a	164	2
624.4.bg	\(\chi_{624}(281, \cdot)\)	None	0	2
624.4.bh	\(\chi_{624}(131, \cdot)\)	n/a	576	2
624.4.bj	\(\chi_{624}(181, \cdot)\)	n/a	336	2
624.4.bm	\(\chi_{624}(317, \cdot)\)	n/a	664	2
624.4.bn	\(\chi_{624}(187, \cdot)\)	n/a	336	2
624.4.bq	\(\chi_{624}(23, \cdot)\)	None	0	2
624.4.br	\(\chi_{624}(217, \cdot)\)	None	0	2
624.4.bu	\(\chi_{624}(191, \cdot)\)	n/a	168	2
624.4.bv	\(\chi_{624}(49, \cdot)\)	624.4.bv.a	2	2
		624.4.bv.b	2
		624.4.bv.c	4
		624.4.bv.d	4
		624.4.bv.e	4
		624.4.bv.f	6
		624.4.bv.g	8
		624.4.bv.h	10
		624.4.bv.i	20
		624.4.bv.j	24
624.4.bz	\(\chi_{624}(95, \cdot)\)	n/a	168	2
624.4.ca	\(\chi_{624}(121, \cdot)\)	None	0	2
624.4.cd	\(\chi_{624}(263, \cdot)\)	None	0	2
624.4.ce	\(\chi_{624}(149, \cdot)\)	n/a	1328	4
624.4.ch	\(\chi_{624}(19, \cdot)\)	n/a	672	4
624.4.cj	\(\chi_{624}(205, \cdot)\)	n/a	672	4
624.4.cl	\(\chi_{624}(35, \cdot)\)	n/a	1328	4
624.4.cm	\(\chi_{624}(41, \cdot)\)	None	0	4
624.4.cn	\(\chi_{624}(305, \cdot)\)	n/a	328	4
624.4.cq	\(\chi_{624}(175, \cdot)\)	n/a	168	4
624.4.cr	\(\chi_{624}(7, \cdot)\)	None	0	4
624.4.cv	\(\chi_{624}(61, \cdot)\)	n/a	672	4
624.4.cx	\(\chi_{624}(179, \cdot)\)	n/a	1328	4
624.4.cz	\(\chi_{624}(115, \cdot)\)	n/a	672	4
624.4.da	\(\chi_{624}(245, \cdot)\)	n/a	1328	4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(624))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(624)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 1}\)