Space of modular forms of level 2160, weight 4, and Character 2160.cr

• Label: 2160.4.cr
• Level: $2160$
• Weight: $4$
• Character orbit: 2160.cr
• Rep. character: $\chi_{2160}(197,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1712$
• Sturm bound: $1728$

Defining parameters

Level:	$N$	$=$	$2160 = 2^{4} \cdot 3^{3} \cdot 5$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	2160.cr (of order $12$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$720$
Character field:			$\Q(\zeta_{12})$
Sturm bound:			$1728$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(2160, [\chi])$.

	Total	New	Old
Modular forms	5232	1744	3488
Cusp forms	5136	1712	3424
Eisenstein series	96	32	64

Trace form

1712 * q + 6 * q^2 + 6 * q^5 + 24 * q^10 + 12 * q^11 - 4 * q^16 + 6 * q^20 + 30 * q^22 + 248 * q^28 - 8 * q^31 + 1386 * q^32 + 396 * q^34 + 54 * q^38 + 248 * q^40 - 4 * q^43 - 88 * q^46 + 12 * q^47 + 6 * q^50 - 258 * q^52 + 12 * q^56 - 34 * q^58 - 4 * q^61 - 1368 * q^64 + 12 * q^65 - 4 * q^67 + 390 * q^68 + 14 * q^70 - 96 * q^74 + 1112 * q^76 + 12 * q^77 + 24 * q^82 - 252 * q^85 + 12 * q^86 + 3110 * q^88 - 16 * q^91 - 9456 * q^92 + 12 * q^95 - 4 * q^97

Decomposition of $S_{4}^{\mathrm{new}}(2160, [\chi])$ into newform subspaces

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

Decomposition of $S_{4}^{\mathrm{old}}(2160, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(2160, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(720, [\chi])$$^{\oplus 2}$