Space of modular forms of level 147, weight 8, and Character 147.c

• Label: 147.8.c
• Level: $147$
• Weight: $8$
• Character orbit: 147.c
• Rep. character: $\chi_{147}(146,\cdot)$
• Character field: $\Q$
• Dimension: $90$
• Newform subspaces: $3$
• Sturm bound: $149$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(149\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(147, [\chi])\).

	Total	New	Old
Modular forms	138	98	40
Cusp forms	122	90	32
Eisenstein series	16	8	8

Trace form

90 * q - 5628 * q^4 + 362 * q^9 + 6352 * q^15 + 385780 * q^16 + 34252 * q^18 - 188980 * q^22 + 1117718 * q^25 - 250140 * q^30 + 1835420 * q^36 + 237002 * q^37 + 641114 * q^39 - 1213186 * q^43 - 898000 * q^46 - 6301104 * q^51 + 6746434 * q^57 + 7597884 * q^58 - 1593996 * q^60 - 29942900 * q^64 + 10353614 * q^67 - 12657920 * q^72 + 25802272 * q^78 + 32654142 * q^79 - 16850814 * q^81 - 19127536 * q^85 + 22415780 * q^88 + 6832190 * q^93 - 24714456 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(147, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
147.8.c.a	$147$	$8$	147.c	21.c	$2$	$2$	$2$	$45.921$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					21.8.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+27\beta q^{3}+128 q^{4}-2187 q^{9}+\cdots\)
147.8.c.b	$147$	$8$	147.c	21.c	$2$	$32$	$32$	$45.921$		None					21.8.g.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
147.8.c.c	$147$	$8$	147.c	21.c	$2$	$56$	$56$	$45.921$		None		✓	✓		147.8.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{8}^{\mathrm{old}}(147, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(147, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)