Newform orbit 63.3.j.b

• Label: 63.3.j.b
• Level: $63$
• Weight: $3$
• Character orbit: 63.j
• Analytic conductor: $1.717$
• Analytic rank: $0$
• Dimension: $22$
• CM: no
• Inner twists: $2$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(1.71662566547\)
Analytic rank:	\(0\)
Dimension:	\(22\)
Relative dimension:	\(11\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 22 q - 19 q^{3} - 24 q^{4} + 12 q^{5} - 8 q^{6} - 37 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1		−	3.69072i	−1.07647	−	2.80021i	−9.62138			5.05096	+	2.91617i	−10.3348	+	3.97296i	3.74467	−	5.91417i			20.7469i	−6.68241	+	6.02872i	10.7628	−	18.6416i
11.2		−	3.22356i	−2.32685	+	1.89361i	−6.39137			−4.79167	−	2.76647i	6.10417	+	7.50076i	−6.99696	+	0.206413i			7.70873i	1.82848	−	8.81230i	−8.91790	+	15.4463i
11.3		−	2.41355i	1.94613	+	2.28311i	−1.82523			5.93347	+	3.42569i	5.51041	−	4.69707i	−6.55070	−	2.46747i		−	5.24892i	−1.42519	+	8.88644i	8.26808	−	14.3207i
11.4		−	1.46555i	0.993737	−	2.83063i	1.85217			0.998268	+	0.576350i	−4.14843	−	1.45637i	−4.05935	+	5.70277i		−	8.57663i	−7.02497	−	5.62581i	0.844669	−	1.46301i
11.5		−	1.29088i	−2.37377	+	1.83445i	2.33363			4.18841	+	2.41818i	2.36806	+	3.06425i	6.74202	−	1.88284i		−	8.17595i	2.26955	−	8.70914i	3.12158	−	5.40673i
11.6		−	0.513687i	−2.25960	−	1.97337i	3.73613			−6.08350	−	3.51231i	−1.01370	+	1.16073i	1.23968	−	6.88935i		−	3.97395i	1.21160	+	8.91807i	−1.80423	+	3.12502i
11.7			0.0767494i	0.891547	+	2.86446i	3.99411			−3.53076	−	2.03848i	−0.219846	+	0.0684257i	2.97142	+	6.33803i			0.613543i	−7.41029	+	5.10760i	0.156452	−	0.270983i
11.8			1.28539i	−2.79035	−	1.10178i	2.34778			6.82011	+	3.93759i	1.41622	−	3.58669i	−6.26023	+	3.13201i			8.15936i	6.57215	+	6.14872i	−5.06133	+	8.76649i
11.9			2.15495i	0.867675	−	2.87178i	−0.643801			1.62693	+	0.939308i	6.18854	+	1.86979i	6.99124	+	0.350157i			7.23243i	−7.49428	−	4.98355i	−2.02416	+	3.50595i
11.10			2.74500i	−0.432548	+	2.96865i	−3.53503			2.32531	+	1.34252i	−8.14895	−	1.18734i	0.122457	−	6.99893i			1.27635i	−8.62581	−	2.56817i	−3.68521	+	6.38297i
11.11			2.87176i	−2.93949	+	0.599520i	−4.24700			−6.53753	−	3.77444i	−1.72168	−	8.44150i	2.05575	+	6.69133i		−	0.709334i	8.28115	−	3.52456i	10.8393	−	18.7742i
23.1		−	2.87176i	−2.93949	−	0.599520i	−4.24700			−6.53753	+	3.77444i	−1.72168	+	8.44150i	2.05575	−	6.69133i			0.709334i	8.28115	+	3.52456i	10.8393	+	18.7742i
23.2		−	2.74500i	−0.432548	−	2.96865i	−3.53503			2.32531	−	1.34252i	−8.14895	+	1.18734i	0.122457	+	6.99893i		−	1.27635i	−8.62581	+	2.56817i	−3.68521	−	6.38297i
23.3		−	2.15495i	0.867675	+	2.87178i	−0.643801			1.62693	−	0.939308i	6.18854	−	1.86979i	6.99124	−	0.350157i		−	7.23243i	−7.49428	+	4.98355i	−2.02416	−	3.50595i
23.4		−	1.28539i	−2.79035	+	1.10178i	2.34778			6.82011	−	3.93759i	1.41622	+	3.58669i	−6.26023	−	3.13201i		−	8.15936i	6.57215	−	6.14872i	−5.06133	−	8.76649i
23.5		−	0.0767494i	0.891547	−	2.86446i	3.99411			−3.53076	+	2.03848i	−0.219846	−	0.0684257i	2.97142	−	6.33803i		−	0.613543i	−7.41029	−	5.10760i	0.156452	+	0.270983i
23.6			0.513687i	−2.25960	+	1.97337i	3.73613			−6.08350	+	3.51231i	−1.01370	−	1.16073i	1.23968	+	6.88935i			3.97395i	1.21160	−	8.91807i	−1.80423	−	3.12502i
23.7			1.29088i	−2.37377	−	1.83445i	2.33363			4.18841	−	2.41818i	2.36806	−	3.06425i	6.74202	+	1.88284i			8.17595i	2.26955	+	8.70914i	3.12158	+	5.40673i
23.8			1.46555i	0.993737	+	2.83063i	1.85217			0.998268	−	0.576350i	−4.14843	+	1.45637i	−4.05935	−	5.70277i			8.57663i	−7.02497	+	5.62581i	0.844669	+	1.46301i
23.9			2.41355i	1.94613	−	2.28311i	−1.82523			5.93347	−	3.42569i	5.51041	+	4.69707i	−6.55070	+	2.46747i			5.24892i	−1.42519	−	8.88644i	8.26808	+	14.3207i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
63.j	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	63.3.j.b	✓	22
3.b	odd	2	1		189.3.j.b		22
7.b	odd	2	1		441.3.j.f		22
7.c	even	3	1		63.3.n.b	yes	22
7.c	even	3	1		441.3.r.g		22
7.d	odd	6	1		441.3.n.f		22
7.d	odd	6	1		441.3.r.f		22
9.c	even	3	1		189.3.n.b		22
9.d	odd	6	1		63.3.n.b	yes	22
21.h	odd	6	1		189.3.n.b		22
63.h	even	3	1		189.3.j.b		22
63.i	even	6	1		441.3.j.f		22
63.j	odd	6	1	inner	63.3.j.b	✓	22
63.n	odd	6	1		441.3.r.g		22
63.o	even	6	1		441.3.n.f		22
63.s	even	6	1		441.3.r.f		22

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
63.3.j.b	✓	22	1.a	even	1	1	trivial
63.3.j.b	✓	22	63.j	odd	6	1	inner
63.3.n.b	yes	22	7.c	even	3	1
63.3.n.b	yes	22	9.d	odd	6	1
189.3.j.b		22	3.b	odd	2	1
189.3.j.b		22	63.h	even	3	1
189.3.n.b		22	9.c	even	3	1
189.3.n.b		22	21.h	odd	6	1
441.3.j.f		22	7.b	odd	2	1
441.3.j.f		22	63.i	even	6	1
441.3.n.f		22	7.d	odd	6	1
441.3.n.f		22	63.o	even	6	1
441.3.r.f		22	7.d	odd	6	1
441.3.r.f		22	63.s	even	6	1
441.3.r.g		22	7.c	even	3	1
441.3.r.g		22	63.n	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^22 + 56*T2^20 + 1326*T2^18 + 17369*T2^16 + 138193*T2^14 + 690216*T2^12 + 2161521*T2^10 + 4118832*T2^8 + 4461102*T2^6 + 2354508*T2^4 + 384993*T2^2 + 2187