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

• Label: 4032.2.dk
• Level: $4032$
• Weight: $2$
• Character orbit: 4032.dk
• Rep. character: $\chi_{4032}(377,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $0$
• Newform subspaces: $0$
• Sturm bound: $1536$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$4032 = 2^{6} \cdot 3^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	4032.dk (of order $8$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$672$
Character field:			$\Q(\zeta_{8})$
Newform subspaces:			$0$
Sturm bound:			$1536$
Trace bound:			$0$

Dimensions

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

	Total	New	Old
Modular forms	3136	0	3136
Cusp forms	3008	0	3008
Eisenstein series	128	0	128

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

$S_{2}^{\mathrm{old}}(4032, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(672, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(2016, [\chi])$$^{\oplus 2}$