Space of modular forms of level 400, weight 6, and Character 400.bb

• Label: 400.6.bb
• Level: $400$
• Weight: $6$
• Character orbit: 400.bb
• Rep. character: $\chi_{400}(41,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $0$
• Newform subspaces: $0$
• Sturm bound: $360$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$400 = 2^{4} \cdot 5^{2}$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	400.bb (of order $10$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$200$
Character field:			$\Q(\zeta_{10})$
Newform subspaces:			$0$
Sturm bound:			$360$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{6}(400, [\chi])$.

	Total	New	Old
Modular forms	1216	0	1216
Cusp forms	1184	0	1184
Eisenstein series	32	0	32

Decomposition of $S_{6}^{\mathrm{old}}(400, [\chi])$ into lower level spaces

$S_{6}^{\mathrm{old}}(400, [\chi]) \simeq$ $S_{6}^{\mathrm{new}}(200, [\chi])$$^{\oplus 2}$