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

• Label: 147.4.k
• Level: $147$
• Weight: $4$
• Character orbit: 147.k
• Rep. character: $\chi_{147}(20,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $324$
• 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.k (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 147 \)
Character field:			\(\Q(\zeta_{14})\)
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	348	348	0
Cusp forms	324	324	0
Eisenstein series	24	24	0

Trace form

324 * q - 7 * q^3 + 198 * q^4 - 35 * q^6 - 22 * q^7 + 65 * q^9 - 14 * q^10 + 378 * q^12 - 14 * q^13 + 133 * q^15 - 810 * q^16 - 210 * q^18 - 85 * q^21 + 126 * q^22 - 7 * q^24 - 908 * q^25 + 35 * q^27 + 272 * q^28 + 616 * q^30 - 7 * q^33 + 490 * q^34 + 23 * q^36 + 1432 * q^37 - 339 * q^39 + 490 * q^40 - 2471 * q^42 - 1074 * q^43 - 1771 * q^45 - 2982 * q^46 - 92 * q^49 + 1757 * q^51 + 2618 * q^52 - 7 * q^54 + 4648 * q^55 - 878 * q^57 + 2730 * q^58 - 3759 * q^60 + 1400 * q^61 - 1219 * q^63 + 2 * q^64 - 5523 * q^66 + 1040 * q^67 + 5453 * q^69 + 1876 * q^70 + 1617 * q^72 - 14 * q^73 + 4151 * q^75 - 7686 * q^76 - 2247 * q^78 - 724 * q^79 + 9781 * q^81 - 6104 * q^82 + 5830 * q^84 - 2702 * q^85 + 721 * q^87 + 686 * q^88 + 2387 * q^90 + 1510 * q^91 - 6478 * q^93 + 4942 * q^94 - 5446 * q^96 - 11018 * q^99

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.k.a	$147$	$4$	147.k	147.k	$14$	$12$	$2$	$8.673$	\(\Q(\zeta_{21})\)	\(\Q(\sqrt{-3}) \)		✓			147.4.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(20\)	$2^{6}\cdot 3^{6}$	$\mathrm{U}(1)[D_{14}]$	\(q+\beta_{11} q^{3}-8\beta_{3} q^{4}+(3\beta_{10}+10\beta_{5})q^{7}+\cdots\)
147.4.k.b	$147$	$4$	147.k	147.k	$14$	$312$	$52$	$8.673$		None		✓	✓		147.4.k.b	$4$	$0$	\(0\)	\(-7\)	\(0\)	\(-42\)		$\mathrm{SU}(2)[C_{14}]$