Space of modular forms of level 336 and weight 6

• Label: 336.6
• Level: 336
• Weight: 6
• Dimension: 6164
• Nonzero newspaces: 16
• Sturm bound: 36864
• Trace bound: 8

Defining parameters

Level:	\( N \)	=	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(36864\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(336))\).

	Total	New	Old
Modular forms	15696	6256	9440
Cusp forms	15024	6164	8860
Eisenstein series	672	92	580

Trace form

6164 * q - 23 * q^3 - 104 * q^4 - 76 * q^5 + 220 * q^6 + 150 * q^7 + 984 * q^8 - 945 * q^9 - 1752 * q^10 - 3624 * q^11 + 4 * q^12 + 460 * q^13 - 324 * q^14 + 4482 * q^15 - 8376 * q^16 - 404 * q^17 + 8788 * q^18 - 9670 * q^19 + 15200 * q^20 - 8359 * q^21 - 2464 * q^22 - 2156 * q^23 - 15588 * q^24 + 20272 * q^25 + 25960 * q^26 + 10372 * q^27 + 1896 * q^28 + 28924 * q^29 + 1468 * q^30 - 53698 * q^31 - 88320 * q^32 - 43507 * q^33 - 62248 * q^34 - 31188 * q^35 + 64712 * q^36 + 31918 * q^37 + 144176 * q^38 + 112064 * q^39 + 180824 * q^40 + 21756 * q^41 - 90360 * q^42 - 92496 * q^43 - 145616 * q^44 + 5709 * q^45 + 56128 * q^46 + 27612 * q^47 + 210876 * q^48 + 593108 * q^49 - 107424 * q^50 - 71259 * q^51 + 31440 * q^52 + 13492 * q^53 - 394732 * q^54 + 52832 * q^55 - 340200 * q^56 - 162582 * q^57 - 244928 * q^58 + 17624 * q^59 + 118076 * q^60 + 36582 * q^61 + 237504 * q^62 + 102129 * q^63 + 106408 * q^64 + 445848 * q^65 + 284884 * q^66 - 269430 * q^67 + 399592 * q^68 - 391148 * q^69 - 420432 * q^70 - 253372 * q^71 - 302804 * q^72 - 270322 * q^73 + 189992 * q^74 + 400424 * q^75 - 484472 * q^76 - 35024 * q^77 - 426312 * q^78 + 414798 * q^79 - 1246736 * q^80 + 728015 * q^81 + 333752 * q^82 + 289800 * q^83 + 5084 * q^84 + 814732 * q^85 + 1162336 * q^86 - 448620 * q^87 + 1180008 * q^88 + 189564 * q^89 + 127364 * q^90 - 917028 * q^91 + 965080 * q^92 - 826523 * q^93 + 541832 * q^94 - 527428 * q^95 - 575396 * q^96 - 1038876 * q^97 - 2413264 * q^98 + 1041038 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(336))\)

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
336.6.a	\(\chi_{336}(1, \cdot)\)	336.6.a.a	1	1
		336.6.a.b	1
		336.6.a.c	1
		336.6.a.d	1
		336.6.a.e	1
		336.6.a.f	1
		336.6.a.g	1
		336.6.a.h	1
		336.6.a.i	1
		336.6.a.j	1
		336.6.a.k	1
		336.6.a.l	1
		336.6.a.m	1
		336.6.a.n	1
		336.6.a.o	1
		336.6.a.p	1
		336.6.a.q	1
		336.6.a.r	1
		336.6.a.s	2
		336.6.a.t	2
		336.6.a.u	2
		336.6.a.v	2
		336.6.a.w	2
		336.6.a.x	2
336.6.b	\(\chi_{336}(223, \cdot)\)	336.6.b.a	6	1
		336.6.b.b	6
		336.6.b.c	14
		336.6.b.d	14
336.6.c	\(\chi_{336}(169, \cdot)\)	None	0	1
336.6.h	\(\chi_{336}(239, \cdot)\)	336.6.h.a	20	1
		336.6.h.b	40
336.6.i	\(\chi_{336}(41, \cdot)\)	None	0	1
336.6.j	\(\chi_{336}(71, \cdot)\)	None	0	1
336.6.k	\(\chi_{336}(209, \cdot)\)	336.6.k.a	2	1
		336.6.k.b	4
		336.6.k.c	8
		336.6.k.d	12
		336.6.k.e	12
		336.6.k.f	40
336.6.p	\(\chi_{336}(55, \cdot)\)	None	0	1
336.6.q	\(\chi_{336}(193, \cdot)\)	336.6.q.a	2	2
		336.6.q.b	2
		336.6.q.c	2
		336.6.q.d	2
		336.6.q.e	4
		336.6.q.f	4
		336.6.q.g	4
		336.6.q.h	4
		336.6.q.i	8
		336.6.q.j	8
		336.6.q.k	8
		336.6.q.l	10
		336.6.q.m	10
		336.6.q.n	12
336.6.s	\(\chi_{336}(155, \cdot)\)	n/a	480	2
336.6.u	\(\chi_{336}(139, \cdot)\)	n/a	320	2
336.6.w	\(\chi_{336}(85, \cdot)\)	n/a	240	2
336.6.y	\(\chi_{336}(125, \cdot)\)	n/a	632	2
336.6.bb	\(\chi_{336}(103, \cdot)\)	None	0	2
336.6.bc	\(\chi_{336}(17, \cdot)\)	n/a	156	2
336.6.bd	\(\chi_{336}(23, \cdot)\)	None	0	2
336.6.bi	\(\chi_{336}(89, \cdot)\)	None	0	2
336.6.bj	\(\chi_{336}(95, \cdot)\)	n/a	160	2
336.6.bk	\(\chi_{336}(25, \cdot)\)	None	0	2
336.6.bl	\(\chi_{336}(31, \cdot)\)	336.6.bl.a	2	2
		336.6.bl.b	2
		336.6.bl.c	10
		336.6.bl.d	10
		336.6.bl.e	14
		336.6.bl.f	14
		336.6.bl.g	14
		336.6.bl.h	14
336.6.bo	\(\chi_{336}(5, \cdot)\)	n/a	1264	4
336.6.bq	\(\chi_{336}(37, \cdot)\)	n/a	640	4
336.6.bs	\(\chi_{336}(19, \cdot)\)	n/a	640	4
336.6.bu	\(\chi_{336}(11, \cdot)\)	n/a	1264	4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(336))\) into lower level spaces

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