Space of modular forms of level 40, weight 2, and Character 40.f

• Label: 40.2.f
• Level: $40$
• Weight: $2$
• Character orbit: 40.f
• Rep. character: $\chi_{40}(29,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	40.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(40, [\chi])\).

	Total	New	Old
Modular forms	8	8	0
Cusp forms	4	4	0
Eisenstein series	4	4	0

Trace form

4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 4 * q^10 + 12 * q^14 - 8 * q^15 - 8 * q^16 + 12 * q^20 + 16 * q^24 - 4 * q^25 - 12 * q^30 + 16 * q^31 - 24 * q^34 + 4 * q^36 - 16 * q^40 - 24 * q^44 - 12 * q^46 + 4 * q^49 + 24 * q^50 + 16 * q^54 + 24 * q^55 + 8 * q^60 + 32 * q^64 + 24 * q^66 - 12 * q^70 - 48 * q^71 - 24 * q^74 + 24 * q^76 - 16 * q^79 - 24 * q^80 - 20 * q^81 - 24 * q^84 + 12 * q^86 + 24 * q^89 - 4 * q^90 + 36 * q^94 - 24 * q^95 - 16 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(40, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
40.2.f.a	$40$	$2$	40.f	40.f	$2$	$4$	$4$	$0.319$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓	✓	✓	40.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)