Space of modular forms of level 84, weight 2, and Character 84.e

• Label: 84.2.e
• Level: $84$
• Weight: $2$
• Character orbit: 84.e
• Rep. character: $\chi_{84}(71,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$84 = 2^{2} \cdot 3 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	84.e (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$12$
Character field:			$\Q$
Newform subspaces:			$1$
Sturm bound:			$32$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(84, [\chi])$.

	Total	New	Old
Modular forms	20	12	8
Cusp forms	12	12	0
Eisenstein series	8	0	8

Trace form

12 * q - 4 * q^4 - 6 * q^6 - 4 * q^9 + 4 * q^10 - 6 * q^12 + 4 * q^16 - 8 * q^18 - 16 * q^22 + 2 * q^24 - 12 * q^25 + 8 * q^28 + 20 * q^30 - 16 * q^33 + 32 * q^34 - 20 * q^36 - 16 * q^37 + 20 * q^40 + 10 * q^42 + 24 * q^45 + 46 * q^48 - 12 * q^49 - 28 * q^52 + 10 * q^54 + 16 * q^57 - 32 * q^58 + 28 * q^60 - 16 * q^61 + 20 * q^64 - 12 * q^66 - 24 * q^69 - 12 * q^70 - 32 * q^72 + 24 * q^73 - 60 * q^76 + 20 * q^78 + 28 * q^81 + 8 * q^82 - 14 * q^84 + 40 * q^85 - 56 * q^88 - 80 * q^90 + 24 * q^93 - 34 * q^96 - 24 * q^97

Decomposition of $S_{2}^{\mathrm{new}}(84, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
84.2.e.a	$84$	$2$	84.e	12.b	$2$	$12$	$12$	$0.671$	12.0.$\cdots$.2	None		✓	✓	✓	84.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-\beta _{9}q^{3}+(-\beta _{2}-\beta _{3})q^{4}+\cdots$