Space of modular forms of level 400, weight 3, and Character 400.bk

• Label: 400.3.bk
• Level: $400$
• Weight: $3$
• Character orbit: 400.bk
• Rep. character: $\chi_{400}(11,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $944$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bk (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 400 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(400, [\chi])\).

	Total	New	Old
Modular forms	976	976	0
Cusp forms	944	944	0
Eisenstein series	32	32	0

Trace form

\( 944 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} - 32 q^{7} + 12 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(400, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
400.3.bk.a	$400$	$3$	400.bk	400.ak	$20$	$944$	$118$	$10.899$		None		✓	✓	✓	400.3.bk.a	$4$	$0$	\(-6\)	\(-6\)	\(-8\)	\(-32\)		$\mathrm{SU}(2)[C_{20}]$