Space of modular forms of level 840, weight 4, and Character 840.w

• Label: 840.4.w
• Level: $840$
• Weight: $4$
• Character orbit: 840.w
• Rep. character: $\chi_{840}(139,\cdot)$
• Character field: $\Q$
• Dimension: $288$
• Sturm bound: $768$

Defining parameters

Level:	$N$	$=$	$840 = 2^{3} \cdot 3 \cdot 5 \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	840.w (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$280$
Character field:			$\Q$
Sturm bound:			$768$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(840, [\chi])$.

	Total	New	Old
Modular forms	584	288	296
Cusp forms	568	288	280
Eisenstein series	16	0	16

Trace form

288 * q + 2592 * q^9 - 236 * q^14 - 112 * q^16 - 336 * q^30 - 456 * q^35 - 2264 * q^44 - 48 * q^46 + 3192 * q^50 + 2020 * q^56 + 1032 * q^60 + 1008 * q^64 + 1840 * q^70 + 3184 * q^74 + 23328 * q^81 + 2220 * q^84 - 5240 * q^86 - 1696 * q^91

Decomposition of $S_{4}^{\mathrm{new}}(840, [\chi])$ into newform subspaces

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

Decomposition of $S_{4}^{\mathrm{old}}(840, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(840, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(280, [\chi])$$^{\oplus 2}$