Space of modular forms of level 336 and weight 8

• Label: 336.8
• Level: 336
• Weight: 8
• Dimension: 8648
• Nonzero newspaces: 16
• Sturm bound: 49152
• Trace bound: 8

Defining parameters

Level:	\( N \)	=	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(49152\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(336))\).

	Total	New	Old
Modular forms	21840	8740	13100
Cusp forms	21168	8648	12520
Eisenstein series	672	92	580

Trace form

8648 * q + 49 * q^3 - 744 * q^4 + 556 * q^5 - 356 * q^6 + 310 * q^7 - 4008 * q^8 - 3501 * q^9 + 51880 * q^10 + 7224 * q^11 - 54716 * q^12 - 6060 * q^13 + 44028 * q^14 - 67518 * q^15 + 105544 * q^16 - 2908 * q^17 - 83180 * q^18 + 423530 * q^19 - 164000 * q^20 - 33271 * q^21 + 199520 * q^22 + 15860 * q^23 + 552732 * q^24 + 120668 * q^25 - 727960 * q^26 - 554828 * q^27 - 129944 * q^28 - 137596 * q^29 + 330748 * q^30 + 1987198 * q^31 + 1142400 * q^32 + 1269197 * q^33 + 2377944 * q^34 - 1059396 * q^35 - 1659448 * q^36 - 1512954 * q^37 - 3843152 * q^38 + 481352 * q^39 - 1681576 * q^40 - 67404 * q^41 - 239160 * q^42 + 743392 * q^43 + 9559472 * q^44 + 4850277 * q^45 + 9494848 * q^46 - 1780452 * q^47 - 14789316 * q^48 + 21617960 * q^49 - 22514976 * q^50 - 830547 * q^51 + 12424144 * q^52 + 14313068 * q^53 + 22994708 * q^54 + 4112736 * q^55 + 16622424 * q^56 + 2241354 * q^57 - 544320 * q^58 - 9033416 * q^59 - 14608324 * q^60 - 4590866 * q^61 - 27833664 * q^62 - 5144943 * q^63 - 27106776 * q^64 - 1923576 * q^65 + 23043220 * q^66 - 26846342 * q^67 + 41192168 * q^68 + 19810468 * q^69 - 8754512 * q^70 + 7818916 * q^71 - 23519060 * q^72 - 7158026 * q^73 - 37166936 * q^74 - 11996272 * q^75 + 31791624 * q^76 + 19878608 * q^77 + 63812472 * q^78 - 37450098 * q^79 + 52728176 * q^80 + 54298787 * q^81 + 27861304 * q^82 - 6919704 * q^83 + 5064860 * q^84 + 14768956 * q^85 - 64615840 * q^86 + 79456860 * q^87 - 192984728 * q^88 - 35590668 * q^89 - 56729212 * q^90 - 24905732 * q^91 + 144333272 * q^92 - 584819 * q^93 + 143913352 * q^94 + 123039292 * q^95 - 41289380 * q^96 + 92477132 * q^97 - 53327696 * q^98 + 58349102 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(336))\)

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
336.8.a	\(\chi_{336}(1, \cdot)\)	336.8.a.a	1	1
		336.8.a.b	1
		336.8.a.c	1
		336.8.a.d	1
		336.8.a.e	1
		336.8.a.f	1
		336.8.a.g	1
		336.8.a.h	1
		336.8.a.i	1
		336.8.a.j	1
		336.8.a.k	2
		336.8.a.l	2
		336.8.a.m	2
		336.8.a.n	2
		336.8.a.o	2
		336.8.a.p	2
		336.8.a.q	2
		336.8.a.r	3
		336.8.a.s	3
		336.8.a.t	3
		336.8.a.u	3
		336.8.a.v	3
		336.8.a.w	3
336.8.b	\(\chi_{336}(223, \cdot)\)	336.8.b.a	10	1
		336.8.b.b	10
		336.8.b.c	18
		336.8.b.d	18
336.8.c	\(\chi_{336}(169, \cdot)\)	None	0	1
336.8.h	\(\chi_{336}(239, \cdot)\)	336.8.h.a	28	1
		336.8.h.b	56
336.8.i	\(\chi_{336}(41, \cdot)\)	None	0	1
336.8.j	\(\chi_{336}(71, \cdot)\)	None	0	1
336.8.k	\(\chi_{336}(209, \cdot)\)	n/a	110	1
336.8.p	\(\chi_{336}(55, \cdot)\)	None	0	1
336.8.q	\(\chi_{336}(193, \cdot)\)	n/a	112	2
336.8.s	\(\chi_{336}(155, \cdot)\)	n/a	672	2
336.8.u	\(\chi_{336}(139, \cdot)\)	n/a	448	2
336.8.w	\(\chi_{336}(85, \cdot)\)	n/a	336	2
336.8.y	\(\chi_{336}(125, \cdot)\)	n/a	888	2
336.8.bb	\(\chi_{336}(103, \cdot)\)	None	0	2
336.8.bc	\(\chi_{336}(17, \cdot)\)	n/a	220	2
336.8.bd	\(\chi_{336}(23, \cdot)\)	None	0	2
336.8.bi	\(\chi_{336}(89, \cdot)\)	None	0	2
336.8.bj	\(\chi_{336}(95, \cdot)\)	n/a	224	2
336.8.bk	\(\chi_{336}(25, \cdot)\)	None	0	2
336.8.bl	\(\chi_{336}(31, \cdot)\)	n/a	112	2
336.8.bo	\(\chi_{336}(5, \cdot)\)	n/a	1776	4
336.8.bq	\(\chi_{336}(37, \cdot)\)	n/a	896	4
336.8.bs	\(\chi_{336}(19, \cdot)\)	n/a	896	4
336.8.bu	\(\chi_{336}(11, \cdot)\)	n/a	1776	4

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(336))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(336)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 2}\)