Newform orbit 143.3.v.a

• Label: 143.3.v.a
• Level: $143$
• Weight: $3$
• Character orbit: 143.v
• Analytic conductor: $3.896$
• Analytic rank: $0$
• Dimension: $208$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	143.v (of order \(30\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.89646778035\)
Analytic rank:	\(0\)
Dimension:	\(208\)
Relative dimension:	\(26\) over \(\Q(\zeta_{30})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 208 q - 15 q^{2} - 3 q^{3} + 45 q^{4} - 15 q^{6} - 15 q^{7} + 57 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1	−3.67443	−	0.781024i	−4.92284	+	2.19179i	9.23726	+	4.11269i	−0.471020	−	0.153044i	19.8005	−	4.20872i	3.41812	+	1.52185i	−18.5732	−	13.4942i	13.4083	−	14.8914i	1.61120	+	0.930227i
17.2	−3.51923	−	0.748036i	0.654864	−	0.291564i	8.17125	+	3.63808i	8.76179	+	2.84688i	−2.52272	+	0.536221i	0.402261	+	0.179098i	−14.3922	−	10.4566i	−5.67834	+	6.30643i	−28.7052	−	16.5730i
17.3	−3.48093	−	0.739895i	1.21380	−	0.540417i	7.91527	+	3.52410i	−5.92807	−	1.92615i	−4.62500	+	0.983073i	6.14679	+	2.73673i	−13.4288	−	9.75663i	−4.84092	+	5.37639i	19.2101	+	11.0909i
17.4	−3.15722	−	0.671088i	3.95373	−	1.76031i	5.86351	+	2.61060i	−1.36499	−	0.443513i	−13.6641	+	2.90440i	−12.0103	−	5.34731i	−6.31523	−	4.58828i	6.51107	−	7.23127i	4.01195	+	2.31630i
17.5	−2.85535	−	0.606922i	−0.992517	+	0.441897i	4.13046	+	1.83900i	−0.161630	−	0.0525167i	3.10218	−	0.659388i	−2.66826	−	1.18799i	−1.23124	−	0.894547i	−5.23236	+	5.81112i	0.429635	+	0.248050i
17.6	−2.53262	−	0.538326i	4.66738	−	2.07805i	2.47021	+	1.09981i	1.33263	+	0.432997i	−12.9394	+	2.75035i	8.38486	+	3.73318i	2.71478	+	1.97240i	11.4440	−	12.7098i	−3.14195	−	1.81401i
17.7	−2.13293	−	0.453368i	−3.67536	+	1.63637i	0.689653	+	0.307053i	−6.30001	−	2.04700i	8.58114	−	1.82398i	−8.29142	−	3.69158i	5.72473	+	4.15926i	4.80834	−	5.34020i	12.5094	+	7.22232i
17.8	−2.10701	−	0.447859i	−3.30289	+	1.47054i	0.584730	+	0.260339i	3.97305	+	1.29092i	7.61782	−	1.61922i	3.59085	+	1.59875i	5.85532	+	4.25414i	2.72443	−	3.02578i	−7.79310	−	4.49935i
17.9	−1.70339	−	0.362067i	1.50559	−	0.670332i	−0.883726	−	0.393460i	−7.44226	−	2.41814i	−2.80732	+	0.596714i	3.27364	+	1.45752i	6.99832	+	5.08458i	−4.20472	+	4.66981i	11.8016	+	6.81364i
17.10	−1.26036	−	0.267898i	−0.860765	+	0.383237i	−2.13744	−	0.951651i	5.51109	+	1.79066i	1.18754	−	0.252420i	−7.33675	−	3.26653i	6.60873	+	4.80152i	−5.42813	+	6.02855i	−6.46624	−	3.73329i
17.11	−1.14798	−	0.244010i	2.79128	−	1.24276i	−2.39587	−	1.06671i	4.92315	+	1.59963i	−3.50756	+	0.745556i	4.54621	+	2.02410i	6.28804	+	4.56853i	0.224601	−	0.249445i	−5.26134	−	3.03763i
17.12	−0.408440	−	0.0868167i	−4.00306	+	1.78228i	−3.49490	−	1.55603i	−6.21982	−	2.02094i	1.78974	−	0.380422i	9.80369	+	4.36488i	2.64364	+	1.92071i	6.82582	−	7.58085i	2.36497	+	1.36542i
17.13	−0.306672	−	0.0651851i	1.72928	−	0.769926i	−3.56438	−	1.58697i	−3.40337	−	1.10582i	−0.580510	+	0.123391i	−1.89014	−	0.841546i	2.00423	+	1.45616i	−3.62454	+	4.02546i	0.971634	+	0.560973i
17.14	0.313380	+	0.0666110i	−1.57126	+	0.699572i	−3.56041	−	1.58520i	2.63216	+	0.855240i	−0.539002	+	0.114568i	9.32605	+	4.15222i	−2.04695	−	1.48719i	−4.04271	+	4.48988i	0.767898	+	0.443346i
17.15	0.370063	+	0.0786593i	−4.76181	+	2.12009i	−3.52342	−	1.56873i	5.79080	+	1.88154i	−1.92894	+	0.410008i	−4.38341	−	1.95162i	−2.40480	−	1.74719i	12.1579	−	13.5027i	1.99496	+	1.15179i
17.16	0.448257	+	0.0952799i	5.22083	−	2.32446i	−3.46233	−	1.54153i	−6.36294	−	2.06745i	2.56175	−	0.544516i	−3.41407	−	1.52004i	−2.88813	−	2.09835i	15.8318	−	17.5830i	−2.65525	−	1.53301i
17.17	0.960111	+	0.204078i	−0.381058	+	0.169658i	−2.77402	−	1.23507i	−1.01442	−	0.329604i	−0.400482	+	0.0851250i	−10.1591	−	4.52313i	−5.58771	−	4.05971i	−5.90575	+	6.55900i	−0.906689	−	0.523477i
17.18	0.989469	+	0.210318i	4.36876	−	1.94510i	−2.71937	−	1.21074i	8.69080	+	2.82381i	4.73184	−	1.00578i	−5.62675	−	2.50519i	−5.70961	−	4.14828i	9.28051	−	10.3070i	8.00538	+	4.62191i
17.19	1.76318	+	0.374776i	−1.69770	+	0.755867i	−0.685829	−	0.305351i	−5.87464	−	1.90879i	−3.27664	+	0.696472i	−1.41427	−	0.629673i	−6.92805	−	5.03352i	−3.71131	+	4.12183i	−9.64270	−	5.56721i
17.20	1.87441	+	0.398419i	1.91066	−	0.850682i	−0.299495	−	0.133344i	2.90039	+	0.942395i	3.92030	−	0.833286i	8.48200	+	3.77643i	−6.70949	−	4.87473i	−3.09520	+	3.43757i	5.06107	+	2.92201i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.d	odd	10	1	inner
13.e	even	6	1	inner
143.v	odd	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	143.3.v.a	✓	208
11.d	odd	10	1	inner	143.3.v.a	✓	208
13.e	even	6	1	inner	143.3.v.a	✓	208
143.v	odd	30	1	inner	143.3.v.a	✓	208

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
143.3.v.a	✓	208	1.a	even	1	1	trivial
143.3.v.a	✓	208	11.d	odd	10	1	inner
143.3.v.a	✓	208	13.e	even	6	1	inner
143.3.v.a	✓	208	143.v	odd	30	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(143, [\chi])\).