Space of modular forms of level 2352, weight 4, and Character 2352.dn

• Label: 2352.4.dn
• Level: $2352$
• Weight: $4$
• Character orbit: 2352.dn
• Rep. character: $\chi_{2352}(115,\cdot)$
• Character field: $\Q(\zeta_{84})$
• Dimension: $16128$
• Sturm bound: $1792$

Defining parameters

Level:	$N$	$=$	$2352 = 2^{4} \cdot 3 \cdot 7^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	2352.dn (of order $84$ and degree $24$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$784$
Character field:			$\Q(\zeta_{84})$
Sturm bound:			$1792$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(2352, [\chi])$.

	Total	New	Old
Modular forms	32352	16128	16224
Cusp forms	32160	16128	16032
Eisenstein series	192	0	192

Trace form

16128 * q - 168 * q^8 + 36 * q^10 - 416 * q^14 + 504 * q^22 - 164 * q^28 + 1008 * q^34 - 456 * q^35 + 1332 * q^40 - 660 * q^42 + 9856 * q^44 + 700 * q^46 - 2856 * q^50 - 2160 * q^52 - 3080 * q^56 - 364 * q^58 - 4128 * q^59 + 6888 * q^64 - 4104 * q^66 - 1848 * q^67 + 6060 * q^68 + 6220 * q^70 - 2240 * q^71 - 2156 * q^74 + 4284 * q^76 - 3528 * q^78 - 45144 * q^80 - 108864 * q^81 - 6960 * q^82 + 1800 * q^84 - 5628 * q^86 + 4004 * q^88 - 9104 * q^91 + 9296 * q^92 - 14580 * q^94 - 7740 * q^96 + 16576 * q^98

Decomposition of $S_{4}^{\mathrm{new}}(2352, [\chi])$ into newform subspaces

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

Decomposition of $S_{4}^{\mathrm{old}}(2352, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(2352, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(784, [\chi])$$^{\oplus 2}$