Space of modular forms of level 8800, weight 2, and Character 8800.kn

• Label: 8800.2.kn
• Level: $8800$
• Weight: $2$
• Character orbit: 8800.kn
• Rep. character: $\chi_{8800}(1833,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $0$
• Newform subspaces: $0$
• Sturm bound: $2880$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$8800 = 2^{5} \cdot 5^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	8800.kn (of order $20$ and degree $8$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$4400$
Character field:			$\Q(\zeta_{20})$
Newform subspaces:			$0$
Sturm bound:			$2880$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(8800, [\chi])$.

	Total	New	Old
Modular forms	11584	0	11584
Cusp forms	11456	0	11456
Eisenstein series	128	0	128

Decomposition of $S_{2}^{\mathrm{old}}(8800, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(8800, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(4400, [\chi])$$^{\oplus 2}$