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

• Label: 21.30.e
• Level: $21$
• Weight: $30$
• Character orbit: 21.e
• Rep. character: $\chi_{21}(4,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $78$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	21.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(1\)

Dimensions

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

	Total	New	Old
Modular forms	158	78	80
Cusp forms	150	78	72
Eisenstein series	8	0	8

Trace form

\( 78 q + 17282 q^{2} - 4782969 q^{3} - 11434038378 q^{4} + 12113760982 q^{5} + 313456656384 q^{6} - 1515385457433 q^{7} - 3851100092424 q^{8} - 892194905743479 q^{9} + O(q^{10}) \)

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.e.a	$21$	$30$	21.e	7.c	$3$	$38$	$19$	$111.884$		None		$2$	$0$	\(25025\)	\(90876411\)	\(-2101591778\)	\(-11\!\cdots\!99\)		$\mathrm{SU}(2)[C_{3}]$
21.30.e.b	$21$	$30$	21.e	7.c	$3$	$40$	$20$	$111.884$		None		$2$	$0$	\(-7743\)	\(-95659380\)	\(14215352760\)	\(-368001036334\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{30}^{\mathrm{old}}(21, [\chi])\) into lower level spaces

\( S_{30}^{\mathrm{old}}(21, [\chi]) \cong \) \(S_{30}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)