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

• Label: 147.2.c
• Level: $147$
• Weight: $2$
• Character orbit: 147.c
• Rep. character: $\chi_{147}(146,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• 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.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
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	26	18	8
Cusp forms	10	10	0
Eisenstein series	16	8	8

Trace form

10 * q - 4 * q^4 + 2 * q^9 - 8 * q^15 - 16 * q^16 + 16 * q^18 - 16 * q^22 - 18 * q^25 + 24 * q^30 - 4 * q^36 + 18 * q^37 + 2 * q^39 + 6 * q^43 + 32 * q^46 - 24 * q^51 - 14 * q^57 - 24 * q^60 + 24 * q^64 - 26 * q^67 - 32 * q^72 + 40 * q^78 - 10 * q^79 - 6 * q^81 - 16 * q^85 + 32 * q^88 + 14 * q^93 + 48 * 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.c.a	$147$	$2$	147.c	21.c	$2$	$2$	$2$	$1.174$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					21.2.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{3}+2 q^{4}-3 q^{9}-2\beta q^{12}+\cdots\)
147.2.c.b	$147$	$2$	147.c	21.c	$2$	$8$	$8$	$1.174$	8.0.3288334336.2	None		✓	✓		147.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)