Space of modular forms of level 336 and weight 4

• Label: 336.4
• Level: 336
• Weight: 4
• Dimension: 3680
• Nonzero newspaces: 16
• Sturm bound: 24576
• Trace bound: 8

Defining parameters

Level:	$N$	=	$336 = 2^{4} \cdot 3 \cdot 7$
Weight:	$k$	=	$4$
Nonzero newspaces:			$16$
Sturm bound:			$24576$
Trace bound:			$8$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(\Gamma_1(336))$.

	Total	New	Old
Modular forms	9552	3772	5780
Cusp forms	8880	3680	5200
Eisenstein series	672	92	580

Trace form

3680 * q + q^3 + 24 * q^4 - 4 * q^5 - 68 * q^6 - 42 * q^7 - 168 * q^8 - 117 * q^9 - 280 * q^10 + 120 * q^11 + 196 * q^12 + 4 * q^13 + 348 * q^14 - 318 * q^15 + 584 * q^16 + 52 * q^17 - 44 * q^18 + 458 * q^19 - 160 * q^20 + 425 * q^21 - 1376 * q^22 + 244 * q^23 - 228 * q^24 - 572 * q^25 + 40 * q^26 + 148 * q^27 + 616 * q^28 - 716 * q^29 + 1468 * q^30 + 702 * q^31 + 1920 * q^32 - 1075 * q^33 + 344 * q^34 + 924 * q^35 + 968 * q^36 - 746 * q^37 - 2512 * q^38 - 1384 * q^39 - 4776 * q^40 - 828 * q^41 - 3960 * q^42 - 2048 * q^43 - 6992 * q^44 + 117 * q^45 - 2688 * q^46 + 540 * q^47 - 1476 * q^48 + 8448 * q^49 + 2784 * q^50 + 2205 * q^51 + 6608 * q^52 + 2236 * q^53 + 5492 * q^54 + 96 * q^55 + 7896 * q^56 + 522 * q^57 + 5184 * q^58 + 3320 * q^59 + 6716 * q^60 + 3742 * q^61 + 4800 * q^62 + 177 * q^63 + 1320 * q^64 - 4056 * q^65 - 2540 * q^66 + 6554 * q^67 - 8984 * q^68 - 764 * q^69 - 7952 * q^70 + 356 * q^71 + 2476 * q^72 + 9638 * q^73 + 5480 * q^74 - 2752 * q^75 + 4872 * q^76 - 2672 * q^77 + 6456 * q^78 - 12082 * q^79 - 1424 * q^80 + 2939 * q^81 - 1480 * q^82 - 11736 * q^83 + 284 * q^84 - 10404 * q^85 + 3424 * q^86 - 1236 * q^87 - 9880 * q^88 + 132 * q^89 - 6652 * q^90 - 6148 * q^91 - 4136 * q^92 + 2941 * q^93 + 6280 * q^94 - 7108 * q^95 - 6308 * q^96 + 1276 * q^97 + 5168 * q^98 - 9682 * q^99

Decomposition of $S_{4}^{\mathrm{new}}(\Gamma_1(336))$

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
336.4.a	$\chi_{336}(1, \cdot)$	336.4.a.a	1	1
		336.4.a.b	1
		336.4.a.c	1
		336.4.a.d	1
		336.4.a.e	1
		336.4.a.f	1
		336.4.a.g	1
		336.4.a.h	1
		336.4.a.i	1
		336.4.a.j	1
		336.4.a.k	1
		336.4.a.l	1
		336.4.a.m	2
		336.4.a.n	2
		336.4.a.o	2
336.4.b	$\chi_{336}(223, \cdot)$	336.4.b.a	2	1
		336.4.b.b	2
		336.4.b.c	2
		336.4.b.d	2
		336.4.b.e	8
		336.4.b.f	8
336.4.c	$\chi_{336}(169, \cdot)$	None	0	1
336.4.h	$\chi_{336}(239, \cdot)$	336.4.h.a	12	1
		336.4.h.b	24
336.4.i	$\chi_{336}(41, \cdot)$	None	0	1
336.4.j	$\chi_{336}(71, \cdot)$	None	0	1
336.4.k	$\chi_{336}(209, \cdot)$	336.4.k.a	2	1
		336.4.k.b	4
		336.4.k.c	8
		336.4.k.d	8
		336.4.k.e	24
336.4.p	$\chi_{336}(55, \cdot)$	None	0	1
336.4.q	$\chi_{336}(193, \cdot)$	336.4.q.a	2	2
		336.4.q.b	2
		336.4.q.c	2
		336.4.q.d	2
		336.4.q.e	2
		336.4.q.f	2
		336.4.q.g	4
		336.4.q.h	4
		336.4.q.i	4
		336.4.q.j	4
		336.4.q.k	6
		336.4.q.l	6
		336.4.q.m	8
336.4.s	$\chi_{336}(155, \cdot)$	n/a	288	2
336.4.u	$\chi_{336}(139, \cdot)$	n/a	192	2
336.4.w	$\chi_{336}(85, \cdot)$	n/a	144	2
336.4.y	$\chi_{336}(125, \cdot)$	n/a	376	2
336.4.bb	$\chi_{336}(103, \cdot)$	None	0	2
336.4.bc	$\chi_{336}(17, \cdot)$	336.4.bc.a	2	2
		336.4.bc.b	2
		336.4.bc.c	12
		336.4.bc.d	12
		336.4.bc.e	16
		336.4.bc.f	48
336.4.bd	$\chi_{336}(23, \cdot)$	None	0	2
336.4.bi	$\chi_{336}(89, \cdot)$	None	0	2
336.4.bj	$\chi_{336}(95, \cdot)$	336.4.bj.a	2	2
		336.4.bj.b	2
		336.4.bj.c	2
		336.4.bj.d	2
		336.4.bj.e	28
		336.4.bj.f	28
		336.4.bj.g	32
336.4.bk	$\chi_{336}(25, \cdot)$	None	0	2
336.4.bl	$\chi_{336}(31, \cdot)$	336.4.bl.a	2	2
		336.4.bl.b	2
		336.4.bl.c	2
		336.4.bl.d	2
		336.4.bl.e	6
		336.4.bl.f	6
		336.4.bl.g	6
		336.4.bl.h	6
		336.4.bl.i	8
		336.4.bl.j	8
336.4.bo	$\chi_{336}(5, \cdot)$	n/a	752	4
336.4.bq	$\chi_{336}(37, \cdot)$	n/a	384	4
336.4.bs	$\chi_{336}(19, \cdot)$	n/a	384	4
336.4.bu	$\chi_{336}(11, \cdot)$	n/a	752	4

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

Decomposition of $S_{4}^{\mathrm{old}}(\Gamma_1(336))$ into lower level spaces

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