Space of modular forms of level 936 and weight 4

• Label: 936.4
• Level: 936
• Weight: 4
• Dimension: 31735
• Nonzero newspaces: 45
• Sturm bound: 193536
• Trace bound: 31

Defining parameters

Level:	\( N \)	=	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 45 \)
Sturm bound:			\(193536\)
Trace bound:			\(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(936))\).

	Total	New	Old
Modular forms	73728	32131	41597
Cusp forms	71424	31735	39689
Eisenstein series	2304	396	1908

Trace form

31735 * q - 28 * q^2 - 42 * q^3 - 8 * q^4 + 44 * q^5 - 8 * q^6 + 48 * q^7 - 88 * q^8 - 138 * q^9 - 268 * q^10 - 250 * q^11 - 260 * q^12 - 64 * q^13 - 364 * q^14 - 96 * q^15 - 304 * q^16 + 71 * q^17 + 192 * q^18 + 60 * q^19 + 872 * q^20 - 456 * q^21 + 1208 * q^22 - 300 * q^23 + 480 * q^24 + 285 * q^25 - 68 * q^26 - 672 * q^27 + 196 * q^28 + 579 * q^29 - 284 * q^30 - 32 * q^31 - 368 * q^32 + 842 * q^33 - 2800 * q^34 + 72 * q^35 + 1484 * q^36 + 15 * q^37 - 824 * q^38 + 228 * q^39 + 2196 * q^40 + 1853 * q^41 + 188 * q^42 + 3986 * q^43 + 2340 * q^44 - 892 * q^45 + 2764 * q^46 + 1500 * q^47 + 1544 * q^48 - 2018 * q^49 + 908 * q^50 - 738 * q^51 - 3982 * q^52 - 5644 * q^53 - 1296 * q^54 - 6516 * q^55 - 8632 * q^56 - 3170 * q^57 - 10496 * q^58 - 8554 * q^59 - 1644 * q^60 + 2959 * q^61 - 5096 * q^62 + 3968 * q^63 + 3652 * q^64 + 9785 * q^65 - 5096 * q^66 + 6234 * q^67 + 3684 * q^68 + 7060 * q^69 + 14268 * q^70 + 6988 * q^71 - 1956 * q^72 - 5604 * q^73 + 2960 * q^74 + 3190 * q^75 + 2448 * q^76 - 8568 * q^77 - 3994 * q^78 - 13064 * q^79 - 16356 * q^80 - 10210 * q^81 - 17916 * q^82 - 23240 * q^83 - 352 * q^84 - 3361 * q^85 - 10072 * q^86 - 12900 * q^87 - 17116 * q^88 + 488 * q^89 - 3788 * q^90 + 14628 * q^91 - 252 * q^92 + 4244 * q^93 + 11316 * q^94 + 22748 * q^95 + 8016 * q^96 - 1146 * q^97 + 28500 * q^98 + 14868 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(936))\)

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
936.4.a	\(\chi_{936}(1, \cdot)\)	936.4.a.a	1	1
		936.4.a.b	1
		936.4.a.c	2
		936.4.a.d	2
		936.4.a.e	2
		936.4.a.f	2
		936.4.a.g	2
		936.4.a.h	2
		936.4.a.i	2
		936.4.a.j	2
		936.4.a.k	3
		936.4.a.l	3
		936.4.a.m	3
		936.4.a.n	4
		936.4.a.o	4
		936.4.a.p	5
		936.4.a.q	5
936.4.c	\(\chi_{936}(649, \cdot)\)	936.4.c.a	10	1
		936.4.c.b	10
		936.4.c.c	12
		936.4.c.d	20
936.4.d	\(\chi_{936}(287, \cdot)\)	None	0	1
936.4.g	\(\chi_{936}(469, \cdot)\)	n/a	180	1
936.4.h	\(\chi_{936}(467, \cdot)\)	n/a	168	1
936.4.j	\(\chi_{936}(755, \cdot)\)	n/a	144	1
936.4.m	\(\chi_{936}(181, \cdot)\)	n/a	208	1
936.4.n	\(\chi_{936}(935, \cdot)\)	None	0	1
936.4.q	\(\chi_{936}(313, \cdot)\)	n/a	216	2
936.4.r	\(\chi_{936}(601, \cdot)\)	n/a	252	2
936.4.s	\(\chi_{936}(529, \cdot)\)	n/a	252	2
936.4.t	\(\chi_{936}(217, \cdot)\)	n/a	106	2
936.4.w	\(\chi_{936}(307, \cdot)\)	n/a	416	2
936.4.x	\(\chi_{936}(343, \cdot)\)	None	0	2
936.4.ba	\(\chi_{936}(161, \cdot)\)	936.4.ba.a	40	2
		936.4.ba.b	44
936.4.bb	\(\chi_{936}(125, \cdot)\)	n/a	336	2
936.4.bd	\(\chi_{936}(179, \cdot)\)	n/a	336	2
936.4.be	\(\chi_{936}(685, \cdot)\)	n/a	416	2
936.4.bh	\(\chi_{936}(503, \cdot)\)	None	0	2
936.4.bi	\(\chi_{936}(361, \cdot)\)	n/a	104	2
936.4.bk	\(\chi_{936}(277, \cdot)\)	n/a	1000	2
936.4.bn	\(\chi_{936}(419, \cdot)\)	n/a	1000	2
936.4.bp	\(\chi_{936}(95, \cdot)\)	None	0	2
936.4.br	\(\chi_{936}(311, \cdot)\)	None	0	2
936.4.bv	\(\chi_{936}(347, \cdot)\)	n/a	1000	2
936.4.bx	\(\chi_{936}(493, \cdot)\)	n/a	1000	2
936.4.by	\(\chi_{936}(131, \cdot)\)	n/a	864	2
936.4.ca	\(\chi_{936}(205, \cdot)\)	n/a	1000	2
936.4.ce	\(\chi_{936}(23, \cdot)\)	None	0	2
936.4.cg	\(\chi_{936}(191, \cdot)\)	None	0	2
936.4.ch	\(\chi_{936}(49, \cdot)\)	n/a	252	2
936.4.cj	\(\chi_{936}(133, \cdot)\)	n/a	1000	2
936.4.cl	\(\chi_{936}(155, \cdot)\)	n/a	1000	2
936.4.co	\(\chi_{936}(157, \cdot)\)	n/a	864	2
936.4.cq	\(\chi_{936}(563, \cdot)\)	n/a	1000	2
936.4.cr	\(\chi_{936}(121, \cdot)\)	n/a	252	2
936.4.ct	\(\chi_{936}(599, \cdot)\)	None	0	2
936.4.cw	\(\chi_{936}(25, \cdot)\)	n/a	252	2
936.4.cy	\(\chi_{936}(263, \cdot)\)	None	0	2
936.4.da	\(\chi_{936}(491, \cdot)\)	n/a	1000	2
936.4.db	\(\chi_{936}(61, \cdot)\)	n/a	1000	2
936.4.df	\(\chi_{936}(647, \cdot)\)	None	0	2
936.4.dg	\(\chi_{936}(829, \cdot)\)	n/a	416	2
936.4.dj	\(\chi_{936}(35, \cdot)\)	n/a	336	2
936.4.dk	\(\chi_{936}(31, \cdot)\)	None	0	4
936.4.dl	\(\chi_{936}(187, \cdot)\)	n/a	2000	4
936.4.dq	\(\chi_{936}(197, \cdot)\)	n/a	672	4
936.4.dr	\(\chi_{936}(89, \cdot)\)	n/a	168	4
936.4.ds	\(\chi_{936}(353, \cdot)\)	n/a	504	4
936.4.dt	\(\chi_{936}(149, \cdot)\)	n/a	2000	4
936.4.dy	\(\chi_{936}(461, \cdot)\)	n/a	2000	4
936.4.dz	\(\chi_{936}(41, \cdot)\)	n/a	504	4
936.4.ec	\(\chi_{936}(271, \cdot)\)	None	0	4
936.4.ed	\(\chi_{936}(19, \cdot)\)	n/a	832	4
936.4.ee	\(\chi_{936}(115, \cdot)\)	n/a	2000	4
936.4.ef	\(\chi_{936}(175, \cdot)\)	None	0	4
936.4.ek	\(\chi_{936}(7, \cdot)\)	None	0	4
936.4.el	\(\chi_{936}(67, \cdot)\)	n/a	2000	4
936.4.em	\(\chi_{936}(5, \cdot)\)	n/a	2000	4
936.4.en	\(\chi_{936}(281, \cdot)\)	n/a	504	4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(936))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(936)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 2}\)