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

• Label: 40.2.k
• Level: $40$
• Weight: $2$
• Character orbit: 40.k
• Rep. character: $\chi_{40}(3,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $8$
• 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.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q(i)\)
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	16	16	0
Cusp forms	8	8	0
Eisenstein series	8	8	0

Trace form

8 * q - 2 * q^2 - 4 * q^3 - 8 * q^6 + 4 * q^8 - 10 * q^10 - 8 * q^11 + 12 * q^12 + 8 * q^16 - 8 * q^17 + 10 * q^18 + 12 * q^22 + 20 * q^26 + 8 * q^27 - 20 * q^28 + 20 * q^30 - 32 * q^32 - 16 * q^33 + 20 * q^35 - 20 * q^36 - 4 * q^38 - 20 * q^40 - 8 * q^41 - 20 * q^42 + 28 * q^43 - 40 * q^46 + 16 * q^48 - 10 * q^50 + 8 * q^51 + 20 * q^52 + 40 * q^56 + 8 * q^57 + 20 * q^58 + 20 * q^60 + 40 * q^62 + 8 * q^66 - 28 * q^67 - 4 * q^68 + 20 * q^70 - 20 * q^72 + 16 * q^73 - 60 * q^75 - 8 * q^76 - 40 * q^78 + 32 * q^81 - 28 * q^82 - 44 * q^83 - 24 * q^86 + 16 * q^88 - 10 * q^90 - 40 * q^91 + 20 * q^92 + 32 * q^96 + 16 * q^97 - 6 * q^98

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.k.a	$40$	$2$	40.k	40.k	$4$	$8$	$4$	$0.319$	\(\Q(\zeta_{20})\)	None		✓	✓	✓	40.2.k.a	$4$	$0$	\(-2\)	\(-4\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta_{7} q^{2}+(-\beta_{6}+\beta_{5}+\beta_{3}-1)q^{3}+\cdots\)