Space of modular forms of level 616 and weight 4

• Label: 616.4
• Level: 616
• Weight: 4
• Dimension: 18142
• Nonzero newspaces: 24
• Sturm bound: 92160
• Trace bound: 8

Defining parameters

Level:	\( N \)	=	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(92160\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(616))\).

	Total	New	Old
Modular forms	35280	18502	16778
Cusp forms	33840	18142	15698
Eisenstein series	1440	360	1080

Trace form

18142 * q - 36 * q^2 - 44 * q^3 - 76 * q^4 - 8 * q^5 + 84 * q^6 - 22 * q^7 + 84 * q^8 - 24 * q^9 - 252 * q^10 - 164 * q^11 - 292 * q^12 - 68 * q^13 - 6 * q^14 + 560 * q^15 + 36 * q^16 - 344 * q^18 - 638 * q^19 - 624 * q^20 - 276 * q^21 - 346 * q^22 - 1636 * q^23 + 604 * q^24 - 40 * q^25 + 2592 * q^26 + 2134 * q^27 + 2746 * q^28 + 1492 * q^29 + 1000 * q^30 + 4052 * q^31 - 2796 * q^32 - 1072 * q^33 - 4796 * q^34 - 2012 * q^35 - 4808 * q^36 - 1908 * q^37 - 2500 * q^38 - 2704 * q^39 + 3708 * q^40 - 1156 * q^41 + 6616 * q^42 - 668 * q^43 + 8170 * q^44 - 824 * q^45 + 8468 * q^46 + 5012 * q^47 + 7840 * q^48 - 1566 * q^49 - 2140 * q^50 + 5026 * q^51 - 9812 * q^52 + 6620 * q^53 - 16836 * q^54 + 268 * q^55 - 9868 * q^56 + 3006 * q^57 - 10940 * q^58 + 802 * q^59 - 11420 * q^60 + 1408 * q^61 - 3224 * q^62 - 4580 * q^63 + 3656 * q^64 - 3976 * q^65 + 1634 * q^66 - 15192 * q^67 - 2716 * q^68 - 15800 * q^69 + 2224 * q^70 - 19244 * q^71 + 14788 * q^72 - 12592 * q^73 + 13448 * q^74 - 9566 * q^75 + 12628 * q^76 + 2176 * q^77 + 11688 * q^78 + 7616 * q^79 + 3964 * q^80 + 12302 * q^81 + 796 * q^82 + 31102 * q^83 + 9786 * q^84 + 22088 * q^85 - 6452 * q^86 + 35236 * q^87 - 22666 * q^88 + 11256 * q^89 - 13944 * q^90 + 17412 * q^91 + 1576 * q^92 + 10360 * q^93 - 3364 * q^94 + 8656 * q^95 - 2144 * q^96 - 5674 * q^97 - 5820 * q^98 - 15532 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(616))\)

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
616.4.a	\(\chi_{616}(1, \cdot)\)	616.4.a.a	1	1
		616.4.a.b	2
		616.4.a.c	2
		616.4.a.d	2
		616.4.a.e	4
		616.4.a.f	4
		616.4.a.g	5
		616.4.a.h	6
		616.4.a.i	6
		616.4.a.j	7
		616.4.a.k	7
616.4.c	\(\chi_{616}(309, \cdot)\)	n/a	180	1
616.4.e	\(\chi_{616}(153, \cdot)\)	616.4.e.a	72	1
616.4.f	\(\chi_{616}(351, \cdot)\)	None	0	1
616.4.h	\(\chi_{616}(419, \cdot)\)	n/a	240	1
616.4.j	\(\chi_{616}(111, \cdot)\)	None	0	1
616.4.l	\(\chi_{616}(43, \cdot)\)	n/a	216	1
616.4.o	\(\chi_{616}(461, \cdot)\)	n/a	284	1
616.4.q	\(\chi_{616}(177, \cdot)\)	n/a	120	2
616.4.r	\(\chi_{616}(113, \cdot)\)	n/a	216	4
616.4.s	\(\chi_{616}(285, \cdot)\)	n/a	568	2
616.4.w	\(\chi_{616}(199, \cdot)\)	None	0	2
616.4.y	\(\chi_{616}(219, \cdot)\)	n/a	568	2
616.4.ba	\(\chi_{616}(263, \cdot)\)	None	0	2
616.4.bc	\(\chi_{616}(243, \cdot)\)	n/a	480	2
616.4.bd	\(\chi_{616}(221, \cdot)\)	n/a	480	2
616.4.bf	\(\chi_{616}(241, \cdot)\)	n/a	144	2
616.4.bi	\(\chi_{616}(13, \cdot)\)	n/a	1136	4
616.4.bl	\(\chi_{616}(211, \cdot)\)	n/a	864	4
616.4.bn	\(\chi_{616}(223, \cdot)\)	None	0	4
616.4.bp	\(\chi_{616}(27, \cdot)\)	n/a	1136	4
616.4.br	\(\chi_{616}(127, \cdot)\)	None	0	4
616.4.bs	\(\chi_{616}(41, \cdot)\)	n/a	288	4
616.4.bu	\(\chi_{616}(141, \cdot)\)	n/a	864	4
616.4.bw	\(\chi_{616}(9, \cdot)\)	n/a	576	8
616.4.by	\(\chi_{616}(17, \cdot)\)	n/a	576	8
616.4.ca	\(\chi_{616}(37, \cdot)\)	n/a	2272	8
616.4.cb	\(\chi_{616}(3, \cdot)\)	n/a	2272	8
616.4.cd	\(\chi_{616}(39, \cdot)\)	None	0	8
616.4.cf	\(\chi_{616}(51, \cdot)\)	n/a	2272	8
616.4.ch	\(\chi_{616}(31, \cdot)\)	None	0	8
616.4.cl	\(\chi_{616}(61, \cdot)\)	n/a	2272	8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(616))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(616)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 1}\)