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

• Label: 147.4.e
• Level: $147$
• Weight: $4$
• Character orbit: 147.e
• Rep. character: $\chi_{147}(67,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $40$
• Newform subspaces: $14$
• Sturm bound: $74$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(74\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	128	40	88
Cusp forms	96	40	56
Eisenstein series	32	0	32

Trace form

40 * q - 4 * q^2 - 6 * q^3 - 60 * q^4 + 8 * q^5 + 24 * q^6 - 156 * q^8 - 180 * q^9 - 46 * q^10 + 40 * q^11 - 72 * q^12 + 4 * q^13 + 84 * q^15 - 164 * q^16 + 132 * q^17 - 36 * q^18 - 218 * q^19 - 872 * q^20 - 180 * q^22 + 208 * q^23 - 54 * q^24 - 686 * q^25 + 466 * q^26 + 108 * q^27 + 920 * q^29 + 216 * q^30 - 348 * q^31 + 1050 * q^32 - 150 * q^33 + 552 * q^34 + 1080 * q^36 + 550 * q^37 - 350 * q^38 + 42 * q^39 - 42 * q^40 - 1208 * q^41 - 2076 * q^43 - 1112 * q^44 + 72 * q^45 - 1076 * q^46 - 240 * q^47 + 1872 * q^48 - 920 * q^50 + 48 * q^51 + 260 * q^52 + 2884 * q^53 - 108 * q^54 + 1972 * q^55 - 1140 * q^57 + 418 * q^58 + 1128 * q^59 - 1938 * q^60 - 188 * q^61 - 3636 * q^62 + 2664 * q^64 - 336 * q^65 + 156 * q^66 - 2290 * q^67 + 2028 * q^68 + 1800 * q^69 + 376 * q^71 + 702 * q^72 + 1350 * q^73 + 1534 * q^74 - 738 * q^75 + 4712 * q^76 - 108 * q^78 + 248 * q^79 + 388 * q^80 - 1620 * q^81 - 956 * q^82 - 1992 * q^83 + 2264 * q^85 + 4670 * q^86 - 1050 * q^87 + 6198 * q^88 + 2672 * q^89 + 828 * q^90 - 10360 * q^92 - 3006 * q^93 - 3204 * q^94 - 928 * q^95 - 1914 * q^96 - 1044 * q^97 - 720 * 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.e.a	$147$	$4$	147.e	7.c	$3$	$2$	$1$	$8.673$	\(\Q(\sqrt{-3}) \)	None		✓			147.4.a.f	$2$	$1$	\(-4\)	\(-3\)	\(-18\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-4\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
147.4.e.b	$147$	$4$	147.e	7.c	$3$	$2$	$1$	$8.673$	\(\Q(\sqrt{-3}) \)	None					21.4.a.b	$2$	$0$	\(-4\)	\(-3\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-4\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
147.4.e.c	$147$	$4$	147.e	7.c	$3$	$2$	$1$	$8.673$	\(\Q(\sqrt{-3}) \)	None					21.4.a.b	$2$	$0$	\(-4\)	\(3\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-4\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
147.4.e.d	$147$	$4$	147.e	7.c	$3$	$2$	$1$	$8.673$	\(\Q(\sqrt{-3}) \)	None		✓			147.4.a.f	$2$	$0$	\(-4\)	\(3\)	\(18\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-4\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
147.4.e.e	$147$	$4$	147.e	7.c	$3$	$2$	$1$	$8.673$	\(\Q(\sqrt{-3}) \)	None		✓			147.4.a.d	$2$	$0$	\(1\)	\(-3\)	\(12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
147.4.e.f	$147$	$4$	147.e	7.c	$3$	$2$	$1$	$8.673$	\(\Q(\sqrt{-3}) \)	None		✓			147.4.a.d	$2$	$0$	\(1\)	\(3\)	\(-12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
147.4.e.g	$147$	$4$	147.e	7.c	$3$	$2$	$1$	$8.673$	\(\Q(\sqrt{-3}) \)	None					21.4.a.a	$2$	$0$	\(3\)	\(-3\)	\(-18\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
147.4.e.h	$147$	$4$	147.e	7.c	$3$	$2$	$1$	$8.673$	\(\Q(\sqrt{-3}) \)	None					21.4.e.a	$2$	$0$	\(3\)	\(3\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
147.4.e.i	$147$	$4$	147.e	7.c	$3$	$2$	$1$	$8.673$	\(\Q(\sqrt{-3}) \)	None					21.4.a.a	$2$	$0$	\(3\)	\(3\)	\(18\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
147.4.e.j	$147$	$4$	147.e	7.c	$3$	$4$	$2$	$8.673$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			147.4.a.j	$2$	$0$	\(-2\)	\(-6\)	\(20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}-\beta _{2})q^{2}+3\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
147.4.e.k	$147$	$4$	147.e	7.c	$3$	$4$	$2$	$8.673$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			147.4.a.j	$2$	$0$	\(-2\)	\(6\)	\(-20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}-\beta _{2})q^{2}-3\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
147.4.e.l	$147$	$4$	147.e	7.c	$3$	$4$	$2$	$8.673$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None					21.4.a.c	$2$	$0$	\(3\)	\(-6\)	\(-6\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{3})q^{2}+3\beta _{1}q^{3}+(7\beta _{1}+\cdots)q^{4}+\cdots\)
147.4.e.m	$147$	$4$	147.e	7.c	$3$	$4$	$2$	$8.673$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None					21.4.a.c	$2$	$0$	\(3\)	\(6\)	\(6\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{3})q^{2}-3\beta _{1}q^{3}+(7\beta _{1}+\cdots)q^{4}+\cdots\)
147.4.e.n	$147$	$4$	147.e	7.c	$3$	$6$	$3$	$8.673$	6.0.9924270768.1	None			✓		21.4.e.b	$2$	$0$	\(-1\)	\(-9\)	\(11\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-3+3\beta _{4})q^{3}+(-8+\beta _{1}+\cdots)q^{4}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(147, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)