Newform orbit 63.4.o.a

• Label: 63.4.o.a
• Level: $63$
• Weight: $4$
• Character orbit: 63.o
• Analytic conductor: $3.717$
• Analytic rank: $0$
• Dimension: $44$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.71712033036\)
Analytic rank:	\(0\)
Dimension:	\(44\)
Relative dimension:	\(22\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
20.1	−4.67796	−	2.70082i	−2.75680	−	4.40455i	10.5889	+	18.3405i	3.43953	+	5.95744i	1.00030	+	28.0499i	14.2961	+	11.7738i		−	71.1815i	−11.8001	+	24.2849i		−	37.1582i
20.2	−4.67796	−	2.70082i	2.75680	+	4.40455i	10.5889	+	18.3405i	−3.43953	−	5.95744i	−1.00030	−	28.0499i	−17.3445	−	6.49383i		−	71.1815i	−11.8001	+	24.2849i			37.1582i
20.3	−3.38393	−	1.95371i	−4.35656	+	2.83202i	3.63397	+	6.29422i	5.82670	+	10.0921i	20.2752	−	1.07189i	−2.49865	−	18.3509i			2.86048i	10.9593	−	24.6758i		−	45.5347i
20.4	−3.38393	−	1.95371i	4.35656	−	2.83202i	3.63397	+	6.29422i	−5.82670	−	10.0921i	−20.2752	+	1.07189i	17.1417	−	7.01157i			2.86048i	10.9593	−	24.6758i			45.5347i
20.5	−3.28475	−	1.89645i	−4.97559	+	1.49782i	3.19307	+	5.53055i	−9.97590	−	17.2788i	19.1841	+	4.51602i	−4.13417	+	18.0529i			6.12125i	22.5131	−	14.9051i			75.6753i
20.6	−3.28475	−	1.89645i	4.97559	−	1.49782i	3.19307	+	5.53055i	9.97590	+	17.2788i	−19.1841	−	4.51602i	−13.5672	+	12.6068i			6.12125i	22.5131	−	14.9051i		−	75.6753i
20.7	−2.31807	−	1.33834i	−3.10623	−	4.16549i	−0.417710	−	0.723496i	−0.223284	−	0.386739i	1.62562	+	13.8131i	−7.50759	−	16.9303i			23.6495i	−7.70264	+	25.8780i			1.19532i
20.8	−2.31807	−	1.33834i	3.10623	+	4.16549i	−0.417710	−	0.723496i	0.223284	+	0.386739i	−1.62562	−	13.8131i	18.4159	−	1.96340i			23.6495i	−7.70264	+	25.8780i		−	1.19532i
20.9	−1.10556	−	0.638294i	−0.213646	+	5.19176i	−3.18516	−	5.51686i	1.59510	+	2.76280i	3.55007	−	5.60342i	−13.1775	+	13.0136i			18.3450i	−26.9087	−	2.21839i		−	4.07258i
20.10	−1.10556	−	0.638294i	0.213646	−	5.19176i	−3.18516	−	5.51686i	−1.59510	−	2.76280i	−3.55007	+	5.60342i	−4.68134	+	17.9188i			18.3450i	−26.9087	−	2.21839i			4.07258i
20.11	−0.0847887	−	0.0489528i	−5.17293	−	0.490712i	−3.99521	−	6.91990i	9.06347	+	15.6984i	0.414584	+	0.294836i	12.7516	+	13.4312i			1.56555i	26.5184	+	5.07683i		−	1.77473i
20.12	−0.0847887	−	0.0489528i	5.17293	+	0.490712i	−3.99521	−	6.91990i	−9.06347	−	15.6984i	−0.414584	−	0.294836i	−18.0075	−	4.32762i			1.56555i	26.5184	+	5.07683i			1.77473i
20.13	0.628557	+	0.362898i	−2.99138	+	4.24872i	−3.73661	−	6.47200i	−5.53318	−	9.58374i	−3.42210	+	1.58500i	13.3114	−	12.8765i		−	11.2304i	−9.10332	−	25.4191i		−	8.03191i
20.14	0.628557	+	0.362898i	2.99138	−	4.24872i	−3.73661	−	6.47200i	5.53318	+	9.58374i	3.42210	−	1.58500i	4.49570	−	17.9663i		−	11.2304i	−9.10332	−	25.4191i			8.03191i
20.15	1.93743	+	1.11857i	−5.00204	−	1.40697i	−1.49759	−	2.59390i	−2.75758	−	4.77627i	−8.11730	−	8.32104i	−17.8859	−	4.80585i		−	24.5978i	23.0409	+	14.0754i		−	12.3382i
20.16	1.93743	+	1.11857i	5.00204	+	1.40697i	−1.49759	−	2.59390i	2.75758	+	4.77627i	8.11730	+	8.32104i	13.1049	+	13.0867i		−	24.5978i	23.0409	+	14.0754i			12.3382i
20.17	2.59186	+	1.49641i	−1.03772	−	5.09148i	0.478502	+	0.828790i	−7.80147	−	13.5125i	4.92933	−	14.7493i	17.7116	+	5.41283i		−	21.0785i	−24.8463	+	10.5670i		−	46.6969i
20.18	2.59186	+	1.49641i	1.03772	+	5.09148i	0.478502	+	0.828790i	7.80147	+	13.5125i	−4.92933	+	14.7493i	−13.5435	−	12.6323i		−	21.0785i	−24.8463	+	10.5670i			46.6969i
20.19	3.92583	+	2.26658i	−3.93727	+	3.39086i	6.27474	+	10.8682i	0.0687529	+	0.119084i	−23.1427	+	4.38780i	2.53789	+	18.3455i			20.6235i	4.00416	−	26.7014i			0.623335i
20.20	3.92583	+	2.26658i	3.93727	−	3.39086i	6.27474	+	10.8682i	−0.0687529	−	0.119084i	23.1427	−	4.38780i	−17.1567	+	6.97489i			20.6235i	4.00416	−	26.7014i		−	0.623335i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
9.d	odd	6	1	inner
63.o	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	63.4.o.a	✓	44
3.b	odd	2	1		189.4.o.a		44
7.b	odd	2	1	inner	63.4.o.a	✓	44
9.c	even	3	1		189.4.o.a		44
9.c	even	3	1		567.4.c.c		44
9.d	odd	6	1	inner	63.4.o.a	✓	44
9.d	odd	6	1		567.4.c.c		44
21.c	even	2	1		189.4.o.a		44
63.l	odd	6	1		189.4.o.a		44
63.l	odd	6	1		567.4.c.c		44
63.o	even	6	1	inner	63.4.o.a	✓	44
63.o	even	6	1		567.4.c.c		44

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
63.4.o.a	✓	44	1.a	even	1	1	trivial
63.4.o.a	✓	44	7.b	odd	2	1	inner
63.4.o.a	✓	44	9.d	odd	6	1	inner
63.4.o.a	✓	44	63.o	even	6	1	inner
189.4.o.a		44	3.b	odd	2	1
189.4.o.a		44	9.c	even	3	1
189.4.o.a		44	21.c	even	2	1
189.4.o.a		44	63.l	odd	6	1
567.4.c.c		44	9.c	even	3	1
567.4.c.c		44	9.d	odd	6	1
567.4.c.c		44	63.l	odd	6	1
567.4.c.c		44	63.o	even	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(63, [\chi])\).