Space of modular forms of level 400, weight 2, and Character 400.bd

• Label: 400.2.bd
• Level: $400$
• Weight: $2$
• Character orbit: 400.bd
• Rep. character: $\chi_{400}(3,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $464$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.bd (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 400 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(400, [\chi])\).

	Total	New	Old
Modular forms	496	496	0
Cusp forms	464	464	0
Eisenstein series	32	32	0

Trace form

\( 464 q - 8 q^{2} - 6 q^{3} - 10 q^{4} - 8 q^{5} - 6 q^{6} - 16 q^{7} - 2 q^{8} - 108 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(400, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
400.2.bd.a	$400$	$2$	400.bd	400.ad	$20$	$464$	$58$	$3.194$		None		$2$	$0$	\(-8\)	\(-6\)	\(-8\)	\(-16\)		$\mathrm{SU}(2)[C_{20}]$