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

• Label: 147.2.m
• Level: $147$
• Weight: $2$
• Character orbit: 147.m
• Rep. character: $\chi_{147}(4,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $108$
• 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.m (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
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	252	108	144
Cusp forms	204	108	96
Eisenstein series	48	0	48

Trace form

\( 108 q + q^{3} + 8 q^{4} - 2 q^{5} - 4 q^{6} + 5 q^{7} + 12 q^{8} + 9 q^{9} + O(q^{10}) \)

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.m.a	$147$	$2$	147.m	49.g	$21$	$48$	$4$	$1.174$		None		$2$	$0$	\(-1\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
147.2.m.b	$147$	$2$	147.m	49.g	$21$	$60$	$5$	$1.174$		None		$2$	$0$	\(1\)	\(5\)	\(-2\)	\(5\)		$\mathrm{SU}(2)[C_{21}]$

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

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