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

• Label: 147.4.i
• Level: $147$
• Weight: $4$
• Character orbit: 147.i
• Rep. character: $\chi_{147}(22,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $168$
• Newform subspaces: $2$
• Sturm bound: $74$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(74\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	348	168	180
Cusp forms	324	168	156
Eisenstein series	24	0	24

Trace form

\( 168 q - 112 q^{4} + 16 q^{5} + 12 q^{6} - 14 q^{7} + 84 q^{8} - 252 q^{9} + O(q^{10}) \)

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.i.a	$147$	$4$	147.i	49.e	$7$	$84$	$14$	$8.673$		None		$2$	$0$	\(-2\)	\(42\)	\(22\)	\(0\)		$\mathrm{SU}(2)[C_{7}]$
147.4.i.b	$147$	$4$	147.i	49.e	$7$	$84$	$14$	$8.673$		None		$2$	$0$	\(2\)	\(-42\)	\(-6\)	\(-14\)		$\mathrm{SU}(2)[C_{7}]$

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

\( S_{4}^{\mathrm{old}}(147, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)