Newform orbit 432.3.x.a

• Label: 432.3.x.a
• Level: $432$
• Weight: $3$
• Character orbit: 432.x
• Analytic conductor: $11.771$
• Analytic rank: $0$
• Dimension: $184$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.x (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.7711474204\)
Analytic rank:	\(0\)
Dimension:	\(184\)
Relative dimension:	\(46\) over \(\Q(\zeta_{12})\)
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
125.1	−1.99910	−	0.0600540i		0		3.99279	+	0.240108i	−7.92852	+	2.12444i		0		−8.42400	+	4.86360i	−7.96755	−	0.719782i		0		15.9775	−	3.77083i
125.2	−1.94424	−	0.468982i		0		3.56011	+	1.82362i	0.517104	−	0.138558i		0		10.5540	−	6.09335i	−6.06645	−	5.21518i		0		−1.07035	+	0.0268763i
125.3	−1.93835	+	0.492752i		0		3.51439	−	1.91025i	−1.22916	+	0.329352i		0		0.837167	−	0.483338i	−5.87084	+	5.43445i		0		2.22025	−	1.24407i
125.4	−1.93717	−	0.497372i		0		3.50524	+	1.92699i	5.08604	−	1.36280i		0		−9.00556	+	5.19936i	−5.83182	−	5.47630i		0		−10.5303	+	0.110321i
125.5	−1.93332	+	0.512131i		0		3.47544	−	1.98023i	2.46048	−	0.659283i		0		2.84517	−	1.64266i	−5.70500	+	5.60829i		0		−4.41925	+	2.53469i
125.6	−1.92351	−	0.547812i		0		3.39980	+	2.10745i	2.68051	−	0.718241i		0		−3.19237	+	1.84312i	−5.38508	−	5.91615i		0		−5.54946	−	0.0868707i
125.7	−1.71077	+	1.03599i		0		1.85347	−	3.54467i	7.93365	−	2.12582i		0		−4.39189	+	2.53566i	0.501371	+	7.98427i		0		−11.3703	+	11.8559i
125.8	−1.65125	−	1.12844i		0		1.45327	+	3.72666i	−7.93556	+	2.12633i		0		2.99388	−	1.72852i	1.80558	−	7.79358i		0		15.5030	+	5.44366i
125.9	−1.61311	+	1.18232i		0		1.20425	−	3.81442i	−4.41854	+	1.18394i		0		1.46095	−	0.843480i	2.56726	+	7.57688i		0		5.72780	−	7.13395i
125.10	−1.43029	−	1.39796i		0		0.0914307	+	3.99895i	−3.58315	+	0.960103i		0		2.87499	−	1.65987i	5.45960	−	5.84746i		0		6.46711	+	3.63587i
125.11	−1.41597	+	1.41245i		0		0.00995269	−	3.99999i	−7.30894	+	1.95842i		0		−10.0693	+	5.81351i	5.63570	+	5.67793i		0		7.58307	−	13.0966i
125.12	−1.34550	−	1.47974i		0		−0.379247	+	3.98198i	7.96785	−	2.13498i		0		10.2471	−	5.91616i	6.40256	−	4.79658i		0		−13.8800	−	8.91771i
125.13	−1.31731	+	1.50489i		0		−0.529401	−	3.96481i	4.63766	−	1.24266i		0		6.36669	−	3.67581i	6.66400	+	4.42619i		0		−4.23916	+	8.61614i
125.14	−1.22012	−	1.58471i		0		−1.02259	+	3.86708i	0.432017	−	0.115759i		0		−7.23679	+	4.17816i	7.37588	−	3.09780i		0		−0.710557	−	0.543380i
125.15	−0.927252	+	1.77206i		0		−2.28041	−	3.28630i	−5.06118	+	1.35614i		0		8.88571	−	5.13017i	7.93803	−	0.993796i		0		2.28983	−	10.2262i
125.16	−0.911412	−	1.78026i		0		−2.33866	+	3.24510i	−4.51043	+	1.20857i		0		−7.69955	+	4.44534i	7.90861	+	1.20579i		0		6.26242	+	6.92824i
125.17	−0.904313	+	1.78388i		0		−2.36444	−	3.22637i	6.35235	−	1.70211i		0		1.38176	−	0.797761i	7.89363	−	1.30022i		0		−2.70816	+	12.8711i
125.18	−0.897969	−	1.78708i		0		−2.38730	+	3.20948i	3.11886	−	0.835695i		0		−0.108974	+	0.0629164i	7.87933	+	1.38428i		0		−4.29409	−	4.82321i
125.19	−0.672644	+	1.88349i		0		−3.09510	−	2.53384i	2.96132	−	0.793484i		0		−7.08251	+	4.08909i	6.85437	−	4.12523i		0		−0.497392	+	6.11137i
125.20	−0.266371	+	1.98218i		0		−3.85809	−	1.05599i	−4.55983	+	1.22180i		0		5.29059	−	3.05452i	3.12086	−	7.36616i		0		−1.20723	−	9.36386i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.d	odd	6	1	inner
16.e	even	4	1	inner
144.w	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	432.3.x.a		184
3.b	odd	2	1		144.3.w.a	✓	184
9.c	even	3	1		144.3.w.a	✓	184
9.d	odd	6	1	inner	432.3.x.a		184
16.e	even	4	1	inner	432.3.x.a		184
48.i	odd	4	1		144.3.w.a	✓	184
144.w	odd	12	1	inner	432.3.x.a		184
144.x	even	12	1		144.3.w.a	✓	184

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
144.3.w.a	✓	184	3.b	odd	2	1
144.3.w.a	✓	184	9.c	even	3	1
144.3.w.a	✓	184	48.i	odd	4	1
144.3.w.a	✓	184	144.x	even	12	1
432.3.x.a		184	1.a	even	1	1	trivial
432.3.x.a		184	9.d	odd	6	1	inner
432.3.x.a		184	16.e	even	4	1	inner
432.3.x.a		184	144.w	odd	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(432, [\chi])\).