Space of modular forms of level 4032, weight 2, and Character 4032.r

• Label: 4032.2.r
• Level: $4032$
• Weight: $2$
• Character orbit: 4032.r
• Rep. character: $\chi_{4032}(1345,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $288$
• Sturm bound: $1536$

Defining parameters

Level:	$N$	$=$	$4032 = 2^{6} \cdot 3^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	4032.r (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$9$
Character field:			$\Q(\zeta_{3})$
Sturm bound:			$1536$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(4032, [\chi])$.

	Total	New	Old
Modular forms	1584	288	1296
Cusp forms	1488	288	1200
Eisenstein series	96	0	96

Decomposition of $S_{2}^{\mathrm{new}}(4032, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(4032, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(4032, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(18, [\chi])$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(36, [\chi])$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(63, [\chi])$$^{\oplus 7}$$\oplus$$S_{2}^{\mathrm{new}}(72, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(126, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(144, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(252, [\chi])$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(288, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(504, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(576, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(1008, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(2016, [\chi])$$^{\oplus 2}$