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

• Label: 336.4.u
• Level: $336$
• Weight: $4$
• Character orbit: 336.u
• Rep. character: $\chi_{336}(139,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $192$
• Sturm bound: $256$

Defining parameters

Level:	$N$	$=$	$336 = 2^{4} \cdot 3 \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	336.u (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$112$
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	192	200
Cusp forms	376	192	184
Eisenstein series	16	0	16

Trace form

192 * q - 20 * q^4 - 168 * q^8 + 40 * q^11 + 208 * q^14 - 60 * q^16 + 36 * q^18 + 268 * q^22 - 656 * q^23 - 416 * q^28 - 400 * q^29 - 456 * q^35 - 16 * q^37 - 660 * q^42 - 808 * q^43 - 2964 * q^44 - 1400 * q^46 - 2156 * q^50 + 752 * q^53 + 1540 * q^56 + 284 * q^58 - 1224 * q^60 + 6412 * q^64 + 3288 * q^67 - 3704 * q^70 + 896 * q^71 + 612 * q^72 + 5628 * q^74 - 3456 * q^78 - 15552 * q^81 + 1800 * q^84 + 1396 * q^86 + 1420 * q^88 + 3496 * q^91 + 2600 * q^92 + 448 * q^98 - 360 * 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}$