Space of modular forms of level 21, weight 30, and Character 21.g

• Label: 21.30.g
• Level: $21$
• Weight: $30$
• Character orbit: 21.g
• Rep. character: $\chi_{21}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $150$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
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:			\(80\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{30}(21, [\chi])\).

	Total	New	Old
Modular forms	158	158	0
Cusp forms	150	150	0
Eisenstein series	8	8	0

Trace form

\( 150 q - 3 q^{3} + 19327352830 q^{4} + 1509655161365 q^{7} - 34829554460625 q^{9} + O(q^{10}) \)

Decomposition of \(S_{30}^{\mathrm{new}}(21, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.30.g.a	$21$	$30$	21.g	21.g	$6$	$2$	$1$	$111.884$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(14348907\)	\(0\)	\(-24\!\cdots\!49\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(3^{14}+3^{14}\zeta_{6})q^{3}+(-2^{29}+2^{29}\zeta_{6})q^{4}+\cdots\)
21.30.g.b	$21$	$30$	21.g	21.g	$6$	$148$	$74$	$111.884$		None		$4$	$0$	\(0\)	\(-14348910\)	\(0\)	\(40\!\cdots\!14\)		$\mathrm{SU}(2)[C_{6}]$