Space of modular forms of level 147, weight 6, and Character 147.c

• Label: 147.6.c
• Level: $147$
• Weight: $6$
• Character orbit: 147.c
• Rep. character: $\chi_{147}(146,\cdot)$
• Character field: $\Q$
• Dimension: $62$
• Newform subspaces: $4$
• Sturm bound: $112$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(112\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(147, [\chi])\).

	Total	New	Old
Modular forms	102	70	32
Cusp forms	86	62	24
Eisenstein series	16	8	8

Trace form

\( 62 q - 892 q^{4} + 602 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(147, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
147.6.c.a	$147$	$6$	147.c	21.c	$2$	$2$	$2$	$23.576$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+9\zeta_{6}q^{3}+2^{5}q^{4}-3^{5}q^{9}+288\zeta_{6}q^{12}+\cdots\)
147.6.c.b	$147$	$6$	147.c	21.c	$2$	$4$	$4$	$23.576$	\(\Q(\sqrt{-3}, \sqrt{-17})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{1}q^{2}+(-8\beta _{2}-\beta _{3})q^{3}-6^{2}q^{4}+\cdots\)
147.6.c.c	$147$	$6$	147.c	21.c	$2$	$16$	$16$	$23.576$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{8}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{5}q^{3}+(-11-\beta _{2})q^{4}+\cdots\)
147.6.c.d	$147$	$6$	147.c	21.c	$2$	$40$	$40$	$23.576$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(147, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(147, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)