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

• Label: 147.2.m
• Level: $147$
• Weight: $2$
• Character orbit: 147.m
• Rep. character: $\chi_{147}(4,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $108$
• 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.m (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
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	252	108	144
Cusp forms	204	108	96
Eisenstein series	48	0	48

Trace form

108 * q + q^3 + 8 * q^4 - 2 * q^5 - 4 * q^6 + 5 * q^7 + 12 * q^8 + 9 * q^9 - 4 * q^10 - 20 * q^11 + 2 * q^12 - 2 * q^13 - 2 * q^14 - 10 * q^15 - 2 * q^16 - 14 * q^17 - 55 * q^19 - 48 * q^20 - 4 * q^21 + 10 * q^22 - 8 * q^23 - 42 * q^24 - q^25 - 26 * q^26 - 2 * q^27 - 50 * q^28 + 16 * q^29 - 8 * q^30 - 75 * q^31 - 106 * q^32 - 2 * q^33 - 112 * q^34 - 26 * q^35 - 16 * q^36 - 44 * q^37 + 58 * q^38 + 8 * q^39 + 28 * q^40 + 76 * q^41 + 66 * q^42 + 14 * q^43 + 84 * q^44 + 26 * q^45 - 24 * q^46 + 8 * q^47 + 64 * q^48 + 45 * q^49 - 188 * q^50 + 52 * q^51 + 86 * q^52 + 40 * q^53 + 2 * q^54 - 36 * q^55 + 168 * q^56 + 6 * q^57 + 14 * q^58 + 16 * q^59 + 68 * q^60 + 17 * q^61 + 20 * q^62 - 8 * q^63 - 36 * q^64 - 30 * q^65 - 4 * q^66 - 21 * q^67 - 68 * q^70 - 60 * q^71 - 48 * q^72 - 45 * q^73 - 62 * q^74 - q^75 - 46 * q^76 - 34 * q^77 - 28 * q^78 - 17 * q^79 + 50 * q^80 + 9 * q^81 + 50 * q^82 + 58 * q^83 - 2 * q^84 + 24 * q^85 + 84 * q^86 - 10 * q^87 + 174 * q^88 + 86 * q^89 + 8 * q^90 + 5 * q^91 + 84 * q^92 - 3 * q^93 + 128 * q^94 + 186 * q^95 - 92 * q^96 - 44 * q^97 + 346 * q^98 + 12 * 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.m.a	$147$	$2$	147.m	49.g	$21$	$48$	$4$	$1.174$		None		✓			147.2.m.a	$2$	$0$	\(-1\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
147.2.m.b	$147$	$2$	147.m	49.g	$21$	$60$	$5$	$1.174$		None		✓	✓		147.2.m.b	$2$	$0$	\(1\)	\(5\)	\(-2\)	\(5\)		$\mathrm{SU}(2)[C_{21}]$

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

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