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

• Label: 336.4.bq
• Level: $336$
• Weight: $4$
• Character orbit: 336.bq
• Rep. character: $\chi_{336}(37,\cdot)$
• 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.bq (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 + 12 * q^10 + 40 * q^11 - 416 * q^14 + 60 * q^16 + 36 * q^18 - 160 * q^20 - 32 * q^22 + 344 * q^28 + 800 * q^29 + 1488 * q^31 - 288 * q^34 + 456 * q^35 - 16 * q^37 - 440 * q^38 + 492 * q^40 - 660 * q^42 + 1616 * q^43 - 1732 * q^44 - 700 * q^46 + 1056 * q^48 - 1456 * q^50 + 2376 * q^52 - 752 * q^53 + 3080 * q^56 + 2824 * q^58 - 1376 * q^59 + 1224 * q^60 + 1872 * q^62 - 1792 * q^64 - 1368 * q^66 - 1440 * q^67 - 2020 * q^68 - 3700 * q^70 + 612 * q^72 - 3472 * q^74 - 1224 * q^76 - 3672 * q^78 - 220 * q^80 + 15552 * q^81 + 1740 * q^82 - 1800 * q^84 - 8348 * q^86 + 496 * q^88 + 3496 * q^91 + 4648 * q^92 + 180 * q^94 - 7728 * q^95 + 2580 * q^96 - 796 * 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}$