Space of modular forms of level 336, weight 4, and Character 336.s

• Label: 336.4.s
• Level: $336$
• Weight: $4$
• Character orbit: 336.s
• Rep. character: $\chi_{336}(155,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $288$
• Sturm bound: $256$

Defining parameters

Level:	$N$	$=$	$336 = 2^{4} \cdot 3 \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	336.s (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$48$
Character field:			$\Q(i)$
Sturm bound:			$256$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(336, [\chi])$.

	Total	New	Old
Modular forms	392	288	104
Cusp forms	376	288	88
Eisenstein series	16	0	16

Trace form

288 * q - 60 * q^6 - 120 * q^10 + 156 * q^12 - 24 * q^16 - 48 * q^19 - 432 * q^22 + 736 * q^24 + 264 * q^27 + 48 * q^30 - 696 * q^34 + 1240 * q^36 - 1200 * q^39 + 864 * q^43 - 1272 * q^46 - 2444 * q^48 + 14112 * q^49 + 1008 * q^52 - 576 * q^55 + 600 * q^58 + 1832 * q^60 + 1824 * q^61 + 1080 * q^64 - 836 * q^66 + 1632 * q^67 + 504 * q^70 + 3368 * q^72 - 3304 * q^75 - 3768 * q^76 + 4040 * q^78 - 5088 * q^82 - 480 * q^85 - 2576 * q^87 - 14520 * q^88 + 2248 * q^90 + 4272 * q^93 - 4464 * q^94 - 6176 * q^96 - 5312 * q^99

Decomposition of $S_{4}^{\mathrm{new}}(336, [\chi])$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of $S_{4}^{\mathrm{old}}(336, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(336, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(48, [\chi])$$^{\oplus 2}$