Space of modular forms of level 147, weight 2, and Character 147.i

• Label: 147.2.i
• Level: $147$
• Weight: $2$
• Character orbit: 147.i
• Rep. character: $\chi_{147}(22,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $60$
• Newform subspaces: $2$
• Sturm bound: $37$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.i (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(37\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(147, [\chi])\).

	Total	New	Old
Modular forms	120	60	60
Cusp forms	96	60	36
Eisenstein series	24	0	24

Trace form

\( 60 q - 2 q^{3} - 12 q^{4} - 4 q^{5} - 2 q^{6} - 6 q^{7} - 12 q^{8} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(147, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
147.2.i.a	$147$	$2$	147.i	49.e	$7$	$24$	$4$	$1.174$		None		$2$	$0$	\(1\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{7}]$
147.2.i.b	$147$	$2$	147.i	49.e	$7$	$36$	$6$	$1.174$		None		$2$	$0$	\(-1\)	\(-6\)	\(-4\)	\(-6\)		$\mathrm{SU}(2)[C_{7}]$

Decomposition of \(S_{2}^{\mathrm{old}}(147, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(147, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)