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

• Label: 40.2.d
• Level: $40$
• Weight: $2$
• Character orbit: 40.d
• Rep. character: $\chi_{40}(21,\cdot)$
• 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.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
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	4	4
Cusp forms	4	4	0
Eisenstein series	4	0	4

Trace form

4 * q - 2 * q^2 + 4 * q^6 - 4 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^10 - 4 * q^12 - 4 * q^14 + 4 * q^15 + 8 * q^16 + 14 * q^18 + 4 * q^20 + 4 * q^22 - 4 * q^23 + 8 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 8 * q^30 - 8 * q^31 + 8 * q^32 + 8 * q^33 - 12 * q^34 - 24 * q^36 - 20 * q^38 + 24 * q^39 - 8 * q^40 - 8 * q^41 - 4 * q^42 + 8 * q^44 + 20 * q^46 + 20 * q^47 - 24 * q^48 - 12 * q^49 + 2 * q^50 + 8 * q^54 - 8 * q^55 + 8 * q^56 + 8 * q^57 + 24 * q^58 + 12 * q^60 + 16 * q^62 - 20 * q^63 - 16 * q^66 + 24 * q^68 - 8 * q^70 + 8 * q^71 + 8 * q^72 + 16 * q^73 + 4 * q^74 - 16 * q^76 - 24 * q^78 - 32 * q^79 + 4 * q^81 - 8 * q^82 - 8 * q^84 + 20 * q^86 - 48 * q^87 - 16 * q^88 + 8 * q^89 + 10 * q^90 - 36 * q^92 - 4 * q^94 + 16 * q^95 + 32 * q^96 - 16 * q^97 + 18 * 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.d.a	$40$	$2$	40.d	8.b	$2$	$4$	$4$	$0.319$	\(\Q(\zeta_{12})\)	None		✓	✓	✓	40.2.d.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}-\beta_1)q^{2}+(-\beta_{3}+\beta_{2}+\beta_1-1)q^{3}+\cdots\)