Space of modular forms of level 147, weight 4, and Character 147.c

• Label: 147.4.c
• Level: $147$
• Weight: $4$
• Character orbit: 147.c
• Rep. character: $\chi_{147}(146,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $74$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(74\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(147, [\chi])\).

	Total	New	Old
Modular forms	64	44	20
Cusp forms	48	36	12
Eisenstein series	16	8	8

Trace form

\( 36 q - 124 q^{4} - 58 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(147, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
147.4.c.a	$147$	$4$	147.c	21.c	$2$	$12$	$12$	$8.673$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(-2+\beta _{11})q^{4}+\cdots\)
147.4.c.b	$147$	$4$	147.c	21.c	$2$	$24$	$24$	$8.673$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(147, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(147, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)