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

• Label: 336.4.bs
• Level: $336$
• Weight: $4$
• Character orbit: 336.bs
• Rep. character: $\chi_{336}(19,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $384$
• Sturm bound: $256$

Defining parameters

Level:	$N$	$=$	$336 = 2^{4} \cdot 3 \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	336.bs (of order $12$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$112$
Character field:			$\Q(\zeta_{12})$
Sturm bound:			$256$

Dimensions

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

	Total	New	Old
Modular forms	784	384	400
Cusp forms	752	384	368
Eisenstein series	32	0	32

Trace form

384 * q + 20 * q^4 + 168 * q^8 - 36 * q^10 - 40 * q^11 + 416 * q^14 + 60 * q^16 - 36 * q^18 - 976 * q^22 + 656 * q^23 + 416 * q^28 - 800 * q^29 + 456 * q^35 + 16 * q^37 - 2340 * q^40 + 660 * q^42 - 1616 * q^43 - 732 * q^44 - 700 * q^46 + 4256 * q^50 + 2160 * q^52 - 752 * q^53 + 3080 * q^56 + 808 * q^58 + 4128 * q^59 + 1224 * q^60 - 7840 * q^64 + 4104 * q^66 + 2256 * q^67 - 6060 * q^68 - 6220 * q^70 - 896 * q^71 - 612 * q^72 + 840 * q^74 + 3672 * q^78 - 7524 * q^80 + 15552 * q^81 - 5220 * q^82 - 1800 * q^84 + 8348 * q^86 - 496 * q^88 - 3496 * q^91 - 11432 * q^92 + 7020 * q^94 + 7740 * q^96 + 5516 * q^98 - 720 * 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}}(112, [\chi])$$^{\oplus 2}$