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

• Label: 147.2.e
• Level: $147$
• Weight: $2$
• Character orbit: 147.e
• Rep. character: $\chi_{147}(67,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $14$
• Newform subspaces: $5$
• Sturm bound: $37$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(37\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	54	14	40
Cusp forms	22	14	8
Eisenstein series	32	0	32

Trace form

14 * q + 4 * q^2 + q^3 - 4 * q^4 - 2 * q^5 - 4 * q^6 - 12 * q^8 - 7 * q^9 - 4 * q^10 + 2 * q^11 + 2 * q^12 - 2 * q^13 + 4 * q^15 - 6 * q^16 + 4 * q^18 + q^19 + 8 * q^20 - 8 * q^22 + 8 * q^23 - q^25 + 2 * q^26 - 2 * q^27 - 32 * q^29 + 9 * q^31 + 6 * q^32 - 2 * q^33 + 8 * q^36 + q^37 + 2 * q^38 - 13 * q^39 + 20 * q^41 - 6 * q^43 + 20 * q^44 - 2 * q^45 + 24 * q^46 - 6 * q^47 + 8 * q^48 + 56 * q^50 + 4 * q^51 + 2 * q^52 - 16 * q^53 + 2 * q^54 - 8 * q^55 + 18 * q^57 - 12 * q^58 - 12 * q^59 + 8 * q^60 + 10 * q^61 - 36 * q^62 - 44 * q^64 - 30 * q^65 - 4 * q^66 - 3 * q^67 - 28 * q^71 + 6 * q^72 - 3 * q^73 - 10 * q^74 - q^75 - 4 * q^76 - 36 * q^78 + q^79 + 8 * q^80 - 7 * q^81 - 20 * q^82 - 12 * q^83 + 32 * q^85 - 50 * q^86 + 4 * q^87 - 48 * q^88 + 16 * q^89 + 8 * q^90 + 112 * q^92 + 7 * q^93 - 12 * q^94 + 34 * q^95 - 8 * q^96 + 12 * q^97 - 4 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
147.2.e.a	$147$	$2$	147.e	7.c	$3$	$2$	$1$	$1.174$	\(\Q(\sqrt{-3}) \)	None					21.2.e.a	$2$	$0$	\(-2\)	\(1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
147.2.e.b	$147$	$2$	147.e	7.c	$3$	$2$	$1$	$1.174$	\(\Q(\sqrt{-3}) \)	None					21.2.a.a	$2$	$0$	\(1\)	\(-1\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
147.2.e.c	$147$	$2$	147.e	7.c	$3$	$2$	$1$	$1.174$	\(\Q(\sqrt{-3}) \)	None					21.2.a.a	$2$	$0$	\(1\)	\(1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
147.2.e.d	$147$	$2$	147.e	7.c	$3$	$4$	$2$	$1.174$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			147.2.a.d	$2$	$0$	\(2\)	\(-2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
147.2.e.e	$147$	$2$	147.e	7.c	$3$	$4$	$2$	$1.174$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			147.2.a.d	$2$	$0$	\(2\)	\(2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{2})q^{2}-\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(147, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)