Space of modular forms of level 21, weight 34, and Character 21.c

• Label: 21.34.c
• Level: $21$
• Weight: $34$
• Character orbit: 21.c
• Rep. character: $\chi_{21}(20,\cdot)$
• Character field: $\Q$
• Dimension: $86$
• Newform subspaces: $2$
• Sturm bound: $90$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	21.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(90\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(21, [\chi])\).

	Total	New	Old
Modular forms	90	90	0
Cusp forms	86	86	0
Eisenstein series	4	4	0

Trace form

\( 86 q - 360777252868 q^{4} - 92553563257056 q^{7} + 2201999453496114 q^{9} + O(q^{10}) \)

Decomposition of \(S_{34}^{\mathrm{new}}(21, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.34.c.a	$21$	$34$	21.c	21.c	$2$	$2$	$2$	$144.864$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-15\!\cdots\!40\)	$2\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{14}\zeta_{6}q^{3}+2^{33}q^{4}+(-794875726270+\cdots)q^{7}+\cdots\)
21.34.c.b	$21$	$34$	21.c	21.c	$2$	$84$	$84$	$144.864$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-90\!\cdots\!16\)		$\mathrm{SU}(2)[C_{2}]$