Space of modular forms of level 147, weight 4, and Character 147.m

• Label: 147.4.m
• Level: $147$
• Weight: $4$
• Character orbit: 147.m
• Rep. character: $\chi_{147}(4,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $336$
• Newform subspaces: $2$
• Sturm bound: $74$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(74\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(147, [\chi])\).

	Total	New	Old
Modular forms	696	336	360
Cusp forms	648	336	312
Eisenstein series	48	0	48

Trace form

336 * q - 6 * q^3 + 112 * q^4 + 8 * q^5 + 24 * q^6 + 20 * q^7 - 84 * q^8 + 252 * q^9 - 46 * q^10 - 196 * q^11 - 72 * q^12 + 4 * q^13 + 242 * q^14 - 210 * q^15 + 504 * q^16 - 316 * q^17 + 846 * q^19 + 24 * q^20 - 108 * q^21 - 560 * q^22 + 56 * q^23 + 576 * q^24 + 714 * q^25 - 598 * q^26 + 108 * q^27 + 292 * q^28 + 56 * q^29 + 168 * q^30 + 2256 * q^31 + 2758 * q^32 - 150 * q^33 - 1576 * q^34 - 1960 * q^35 - 2016 * q^36 - 644 * q^37 + 3122 * q^38 + 504 * q^39 + 1470 * q^40 - 760 * q^41 - 180 * q^42 + 28 * q^43 - 9744 * q^44 - 936 * q^45 - 532 * q^46 - 2900 * q^47 - 7536 * q^48 - 1748 * q^49 + 12236 * q^50 - 2184 * q^51 - 5228 * q^52 - 868 * q^53 - 108 * q^54 + 1426 * q^55 + 192 * q^56 - 420 * q^57 + 3038 * q^58 + 764 * q^59 + 6342 * q^60 + 330 * q^61 + 3868 * q^62 + 252 * q^63 + 336 * q^64 - 168 * q^65 + 156 * q^66 - 462 * q^67 + 2028 * q^68 + 1800 * q^69 - 9740 * q^70 + 504 * q^71 + 3024 * q^72 + 4038 * q^73 - 4186 * q^74 - 738 * q^75 + 6854 * q^76 + 1636 * q^77 + 3444 * q^78 + 1148 * q^79 + 9166 * q^80 + 2268 * q^81 + 12974 * q^82 + 13100 * q^83 - 1536 * q^84 - 672 * q^85 + 2772 * q^86 - 4368 * q^87 - 7728 * q^88 + 1552 * q^89 + 828 * q^90 + 2782 * q^91 + 252 * q^92 + 210 * q^93 - 18660 * q^94 - 20832 * q^95 + 3126 * q^96 - 19804 * q^97 - 43186 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(147, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
147.4.m.a	$147$	$4$	147.m	49.g	$21$	$156$	$13$	$8.673$		None		✓			147.4.m.a	$2$	$0$	\(-2\)	\(39\)	\(-3\)	\(7\)		$\mathrm{SU}(2)[C_{21}]$
147.4.m.b	$147$	$4$	147.m	49.g	$21$	$180$	$15$	$8.673$		None		✓	✓		147.4.m.b	$2$	$0$	\(2\)	\(-45\)	\(11\)	\(13\)		$\mathrm{SU}(2)[C_{21}]$

Decomposition of \(S_{4}^{\mathrm{old}}(147, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(147, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)