Newform orbit 63.3.n.b

• Label: 63.3.n.b
• Level: $63$
• Weight: $3$
• Character orbit: 63.n
• 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.n (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.

\(\operatorname{Tr}(f)(q) = \) \( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−3.19625	+	1.84536i	2.96329	+	0.467854i	4.81069	−	8.33236i		−	5.83234i	−10.3348	+	3.97296i	3.24949	−	6.20007i			20.7469i	8.56223	+	2.77278i	10.7628	+	18.6416i
2.2	−2.79169	+	1.61178i	−0.476488	−	2.96192i	3.19568	−	5.53509i			5.53294i	6.10417	+	7.50076i	3.31972	+	6.16275i			7.70873i	−8.54592	+	2.82264i	−8.91790	−	15.4463i
2.3	−2.09020	+	1.20678i	−2.95029	+	0.543839i	0.912615	−	1.58070i		−	6.85138i	5.51041	−	4.69707i	5.41224	+	4.43934i		−	5.24892i	8.40848	−	3.20897i	8.26808	+	14.3207i
2.4	−1.26920	+	0.732774i	1.95453	+	2.27592i	−0.926086	+	1.60403i		−	1.15270i	−4.14843	−	1.45637i	−2.90907	+	6.36689i		−	8.57663i	−1.35961	+	8.89671i	0.844669	+	1.46301i
2.5	−1.11793	+	0.645440i	−0.401800	−	2.97297i	−1.16681	+	2.02098i		−	4.83636i	2.36806	+	3.06425i	−1.74042	−	6.78019i		−	8.17595i	−8.67711	+	2.38908i	3.12158	+	5.40673i
2.6	−0.444866	+	0.256844i	2.83879	−	0.970187i	−1.86806	+	3.23558i			7.02462i	−1.01370	+	1.16073i	5.34652	−	4.51827i		−	3.97395i	7.11748	−	5.50832i	−1.80423	−	3.12502i
2.7	0.0664669	−	0.0383747i	−2.92647	−	0.660129i	−1.99705	+	3.45900i			4.07697i	−0.219846	+	0.0684257i	−6.97461	+	0.595686i			0.613543i	8.12846	+	3.86370i	0.156452	+	0.270983i
2.8	1.11318	−	0.642694i	2.34935	−	1.86563i	−1.17389	+	2.03324i		−	7.87519i	1.41622	−	3.58669i	0.417718	+	6.98753i			8.15936i	2.03887	−	8.76601i	−5.06133	−	8.76649i
2.9	1.86624	−	1.07747i	2.05320	+	2.18732i	0.321900	−	0.557548i		−	1.87862i	6.18854	+	1.86979i	−3.79886	−	5.87951i			7.23243i	−0.568739	+	8.98201i	−2.02416	−	3.50595i
2.10	2.37724	−	1.37250i	−2.35466	−	1.85892i	1.76751	−	3.06142i		−	2.68504i	−8.14895	−	1.18734i	6.00002	−	3.60552i			1.27635i	2.08880	+	8.75425i	−3.68521	−	6.38297i
2.11	2.48702	−	1.43588i	0.950543	−	2.84543i	2.12350	−	3.67801i			7.54889i	−1.72168	−	8.44150i	−6.82274	+	1.56534i		−	0.709334i	−7.19294	−	5.40941i	10.8393	+	18.7742i
32.1	−3.19625	−	1.84536i	2.96329	−	0.467854i	4.81069	+	8.33236i			5.83234i	−10.3348	−	3.97296i	3.24949	+	6.20007i		−	20.7469i	8.56223	−	2.77278i	10.7628	−	18.6416i
32.2	−2.79169	−	1.61178i	−0.476488	+	2.96192i	3.19568	+	5.53509i		−	5.53294i	6.10417	−	7.50076i	3.31972	−	6.16275i		−	7.70873i	−8.54592	−	2.82264i	−8.91790	+	15.4463i
32.3	−2.09020	−	1.20678i	−2.95029	−	0.543839i	0.912615	+	1.58070i			6.85138i	5.51041	+	4.69707i	5.41224	−	4.43934i			5.24892i	8.40848	+	3.20897i	8.26808	−	14.3207i
32.4	−1.26920	−	0.732774i	1.95453	−	2.27592i	−0.926086	−	1.60403i			1.15270i	−4.14843	+	1.45637i	−2.90907	−	6.36689i			8.57663i	−1.35961	−	8.89671i	0.844669	−	1.46301i
32.5	−1.11793	−	0.645440i	−0.401800	+	2.97297i	−1.16681	−	2.02098i			4.83636i	2.36806	−	3.06425i	−1.74042	+	6.78019i			8.17595i	−8.67711	−	2.38908i	3.12158	−	5.40673i
32.6	−0.444866	−	0.256844i	2.83879	+	0.970187i	−1.86806	−	3.23558i		−	7.02462i	−1.01370	−	1.16073i	5.34652	+	4.51827i			3.97395i	7.11748	+	5.50832i	−1.80423	+	3.12502i
32.7	0.0664669	+	0.0383747i	−2.92647	+	0.660129i	−1.99705	−	3.45900i		−	4.07697i	−0.219846	−	0.0684257i	−6.97461	−	0.595686i		−	0.613543i	8.12846	−	3.86370i	0.156452	−	0.270983i
32.8	1.11318	+	0.642694i	2.34935	+	1.86563i	−1.17389	−	2.03324i			7.87519i	1.41622	+	3.58669i	0.417718	−	6.98753i		−	8.15936i	2.03887	+	8.76601i	−5.06133	+	8.76649i
32.9	1.86624	+	1.07747i	2.05320	−	2.18732i	0.321900	+	0.557548i			1.87862i	6.18854	−	1.86979i	−3.79886	+	5.87951i		−	7.23243i	−0.568739	−	8.98201i	−2.02416	+	3.50595i

Inner twists

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

    

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^22 + 6*T2^21 - 10*T2^20 - 132*T2^19 + 63*T2^18 + 1884*T2^17 + 887*T2^16 - 15735*T2^15 - 12503*T2^14 + 93906*T2^13 + 112326*T2^12 - 336231*T2^11 - 485559*T2^10 + 804789*T2^9 + 1590579*T2^8 - 559467*T2^7 - 2151333*T2^6 + 59535*T2^5 + 2181978*T2^4 + 1283040*T2^3 + 175041*T2^2 - 40095*T2 + 2187