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

• Label: 336.4.w
• Level: $336$
• Weight: $4$
• Character orbit: 336.w
• Rep. character: $\chi_{336}(85,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $144$
• Sturm bound: $256$

Defining parameters

Level:	$N$	$=$	$336 = 2^{4} \cdot 3 \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	336.w (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$16$
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	144	248
Cusp forms	376	144	232
Eisenstein series	16	0	16

Trace form

144 * q + 20 * q^4 - 120 * q^10 + 40 * q^11 + 48 * q^12 + 140 * q^14 - 240 * q^15 + 324 * q^16 + 36 * q^18 - 48 * q^19 - 668 * q^22 - 456 * q^24 + 40 * q^26 - 400 * q^29 + 816 * q^30 + 1920 * q^32 + 1696 * q^34 - 216 * q^36 - 16 * q^37 - 2072 * q^38 - 1640 * q^40 - 1672 * q^43 - 1564 * q^44 + 1464 * q^46 - 7056 * q^49 + 2140 * q^50 - 1488 * q^51 + 2736 * q^52 - 752 * q^53 - 216 * q^54 + 196 * q^56 + 444 * q^58 + 1224 * q^60 + 1824 * q^61 + 2928 * q^62 + 504 * q^63 + 476 * q^64 - 1952 * q^65 + 408 * q^67 - 904 * q^68 + 1056 * q^69 + 504 * q^70 + 612 * q^72 + 2484 * q^74 - 2208 * q^75 + 4984 * q^76 - 1904 * q^77 + 72 * q^78 - 11984 * q^79 + 6320 * q^80 - 11664 * q^81 + 3560 * q^82 - 5360 * q^83 + 480 * q^85 + 2028 * q^86 + 6452 * q^88 - 1296 * q^90 + 48 * q^92 - 3704 * q^94 - 600 * q^96 + 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}}(16, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(48, [\chi])$$^{\oplus 2}$$\oplus$$S_{4}^{\mathrm{new}}(112, [\chi])$$^{\oplus 2}$