Space of modular forms of level 21, weight 21, and Character 21.h

• Label: 21.21.h
• Level: $21$
• Weight: $21$
• Character orbit: 21.h
• Rep. character: $\chi_{21}(2,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $102$
• Newform subspaces: $2$
• Sturm bound: $56$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	21.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(56\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	110	110	0
Cusp forms	102	102	0
Eisenstein series	8	8	0

Trace form

\( 102 q - q^{3} + 25165822 q^{4} + 89735164 q^{6} - 92428391 q^{7} + 3283481009 q^{9} + O(q^{10}) \)

Decomposition of \(S_{21}^{\mathrm{new}}(21, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.21.h.a	$21$	$21$	21.h	21.h	$6$	$2$	$1$	$53.238$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(-59049\)	\(0\)	\(-445987849\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q-3^{10}\zeta_{6}q^{3}-2^{20}\zeta_{6}q^{4}+(-122884025+\cdots)q^{7}+\cdots\)
21.21.h.b	$21$	$21$	21.h	21.h	$6$	$100$	$50$	$53.238$		None		$4$	$0$	\(0\)	\(59048\)	\(0\)	\(353559458\)		$\mathrm{SU}(2)[C_{6}]$