Space of modular forms of level 1600, weight 3, and Character 1600.ce

• Label: 1600.3.ce
• Level: $1600$
• Weight: $3$
• Character orbit: 1600.ce
• Rep. character: $\chi_{1600}(73,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $0$
• Newform subspaces: $0$
• Sturm bound: $720$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$1600 = 2^{6} \cdot 5^{2}$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	1600.ce (of order $40$ and degree $16$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$800$
Character field:			$\Q(\zeta_{40})$
Newform subspaces:			$0$
Sturm bound:			$720$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{3}(1600, [\chi])$.

	Total	New	Old
Modular forms	7744	0	7744
Cusp forms	7616	0	7616
Eisenstein series	128	0	128

Decomposition of $S_{3}^{\mathrm{old}}(1600, [\chi])$ into lower level spaces

$S_{3}^{\mathrm{old}}(1600, [\chi]) \simeq$ $S_{3}^{\mathrm{new}}(800, [\chi])$$^{\oplus 2}$