Space of modular forms of level 147, weight 5, and Character 147.d

• Label: 147.5.d
• Level: $147$
• Weight: $5$
• Character orbit: 147.d
• Rep. character: $\chi_{147}(97,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $4$
• Sturm bound: $93$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	147.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(93\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(147, [\chi])\).

	Total	New	Old
Modular forms	82	26	56
Cusp forms	66	26	40
Eisenstein series	16	0	16

Trace form

\( 26 q + 12 q^{2} + 204 q^{4} + 192 q^{8} - 702 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(147, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
147.5.d.a	$147$	$5$	147.d	7.b	$2$	$2$	$2$	$15.195$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-10\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-5q^{2}-3\zeta_{6}q^{3}+9q^{4}-\zeta_{6}q^{5}+15\zeta_{6}q^{6}+\cdots\)
147.5.d.b	$147$	$5$	147.d	7.b	$2$	$2$	$2$	$15.195$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{2}-3\zeta_{6}q^{3}-12q^{4}+6\zeta_{6}q^{5}+\cdots\)
147.5.d.c	$147$	$5$	147.d	7.b	$2$	$6$	$6$	$15.195$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{2}+3\beta _{3}q^{3}+(10+4\beta _{1}+\cdots)q^{4}+\cdots\)
147.5.d.d	$147$	$5$	147.d	7.b	$2$	$16$	$16$	$15.195$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(24\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{4}\cdot 7^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+\beta _{4})q^{2}+\beta _{9}q^{3}+(11+\beta _{1}+2\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(147, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(147, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)