Space of modular forms of level 21, weight 42, and Character 21.g

• Label: 21.42.g
• Level: $21$
• Weight: $42$
• Character orbit: 21.g
• Rep. character: $\chi_{21}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $214$
• Newform subspaces: $2$
• Sturm bound: $112$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(112\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{42}(21, [\chi])\).

	Total	New	Old
Modular forms	222	222	0
Cusp forms	214	214	0
Eisenstein series	8	8	0

Trace form

\( 214 q - 3 q^{3} + 114349209288702 q^{4} - 84099194968875659 q^{7} + 23000002253099910063 q^{9} + O(q^{10}) \)

Decomposition of \(S_{42}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.42.g.a	$21$	$42$	21.g	21.g	$6$	$2$	$1$	$223.591$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(10460353203\)	\(0\)	\(42\!\cdots\!79\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(3^{20}+3^{20}\zeta_{6})q^{3}+(-2^{41}+2^{41}\zeta_{6})q^{4}+\cdots\)
21.42.g.b	$21$	$42$	21.g	21.g	$6$	$212$	$106$	$223.591$		None		$4$	$0$	\(0\)	\(-10460353206\)	\(0\)	\(-50\!\cdots\!38\)		$\mathrm{SU}(2)[C_{6}]$