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

• Label: 84.2.i
• Level: $84$
• Weight: $2$
• Character orbit: 84.i
• Rep. character: $\chi_{84}(25,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $2$
• 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.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
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	44	2	42
Cusp forms	20	2	18
Eisenstein series	24	0	24

Trace form

2 * q + q^3 + 2 * q^5 + q^7 - q^9 - 2 * q^11 - 6 * q^13 + 4 * q^15 - 8 * q^17 + q^19 - 4 * q^21 - 8 * q^23 + q^25 - 2 * q^27 + 8 * q^29 - 3 * q^31 + 2 * q^33 + 10 * q^35 + q^37 - 3 * q^39 + 12 * q^41 + 22 * q^43 + 2 * q^45 - 6 * q^47 - 13 * q^49 + 8 * q^51 + 12 * q^53 - 8 * q^55 + 2 * q^57 - 4 * q^59 + 6 * q^61 - 5 * q^63 - 6 * q^65 - 13 * q^67 - 16 * q^69 - 20 * q^71 + 11 * q^73 - q^75 + 8 * q^77 + 3 * q^79 - q^81 + 4 * q^83 - 32 * q^85 + 4 * q^87 - 3 * q^91 + 3 * q^93 - 2 * q^95 + 20 * q^97 + 4 * q^99

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.i.a	$84$	$2$	84.i	7.c	$3$	$2$	$1$	$0.671$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	84.2.i.a	$2$	$0$	\(0\)	\(1\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{3}+(2-2\zeta_{6})q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(84, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(84, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)