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

• Label: 84.2.f
• Level: $84$
• Weight: $2$
• Character orbit: 84.f
• Rep. character: $\chi_{84}(41,\cdot)$
• Character field: $\Q$
• 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.f (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$21$
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	22	2	20
Cusp forms	10	2	8
Eisenstein series	12	0	12

Trace form

$2 q + 4 q^{7} - 6 q^{9} - 6 q^{21} - 10 q^{25} + 20 q^{37} + 24 q^{39} - 16 q^{43} + 2 q^{49} + 12 q^{57} - 12 q^{63} - 32 q^{67} - 8 q^{79} + 18 q^{81} + 24 q^{91} - 36 q^{93}+O(q^{100})$

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.f.a	$84$	$2$	84.f	21.c	$2$	$2$	$2$	$0.671$	$\Q(\sqrt{-3})$	$\Q(\sqrt{-3})$		✓	✓	✓	84.2.f.a	$4$	$0$	$0$	$0$	$0$	$4$	$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{3}+(-\beta+2)q^{7}-3 q^{9}+4\beta q^{13}+\cdots$

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

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