Newform orbit 143.3.i.a

• Label: 143.3.i.a
• Level: $143$
• Weight: $3$
• Character orbit: 143.i
• Analytic conductor: $3.896$
• Analytic rank: $0$
• Dimension: $52$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	143.i (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.89646778035\)
Analytic rank:	\(0\)
Dimension:	\(52\)
Relative dimension:	\(26\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 52 q - 2 q^{3} - 50 q^{4} - 72 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
10.1	−1.96042	−	3.39554i	1.56909	+	2.71774i	−5.68648	+	9.84926i		−	6.90389i	6.15213	−	10.6558i	0.124727	−	0.216033i	28.9081			−0.424062	+	0.734498i	−23.4425	+	13.5345i
10.2	−1.89361	−	3.27982i	−2.61693	−	4.53266i	−5.17150	+	8.95730i			3.53267i	−9.91088	+	17.1662i	3.17644	−	5.50175i	24.0223			−9.19666	+	15.9291i	11.5865	−	6.68950i
10.3	−1.68273	−	2.91457i	0.337560	+	0.584670i	−3.66315	+	6.34477i			4.79178i	1.13604	−	1.96768i	0.396050	−	0.685979i	11.1946			4.27211	−	7.39951i	13.9660	−	8.06327i
10.4	−1.39823	−	2.42181i	−1.43332	−	2.48258i	−1.91012	+	3.30843i		−	3.08124i	−4.00824	+	6.94247i	−5.97636	+	10.3514i	−0.502684			0.391188	−	0.677557i	−7.46220	+	4.30830i
10.5	−1.39814	−	2.42165i	1.93004	+	3.34294i	−1.90960	+	3.30752i			2.05811i	5.39695	−	9.34779i	−2.50820	+	4.34433i	−0.505587			−2.95015	+	5.10980i	4.98403	−	2.87753i
10.6	−1.35494	−	2.34683i	−1.40344	−	2.43082i	−1.67174	+	2.89553i		−	7.33037i	−3.80315	+	6.58725i	2.28682	−	3.96089i	−1.77911			0.560731	−	0.971215i	−17.2031	+	9.93222i
10.7	−1.06551	−	1.84551i	−0.301239	−	0.521762i	−0.270613	+	0.468715i			4.58168i	−0.641946	+	1.11188i	5.32109	−	9.21640i	−7.37070			4.31851	−	7.47988i	8.45555	−	4.88181i
10.8	−0.880296	−	1.52472i	2.66253	+	4.61163i	0.450158	−	0.779697i		−	4.91448i	4.68762	−	8.11920i	4.54802	−	7.87741i	−8.62746			−9.67810	+	16.7630i	−7.49319	+	4.32620i
10.9	−0.817329	−	1.41565i	−1.94998	−	3.37746i	0.663948	−	1.14999i			9.53698i	−3.18754	+	5.52098i	−4.86541	+	8.42713i	−8.70928			−3.10481	+	5.37768i	13.5011	−	7.79485i
10.10	−0.635631	−	1.10094i	0.944665	+	1.63621i	1.19195	−	2.06451i		−	7.06986i	1.20092	−	2.08005i	−1.65995	+	2.87511i	−8.11560			2.71522	−	4.70289i	−7.78352	+	4.49382i
10.11	−0.366250	−	0.634364i	−0.00402854	−	0.00697764i	1.73172	−	2.99943i			0.645057i	−0.00295091	+	0.00511112i	0.484629	−	0.839402i	−5.46697			4.49997	−	7.79417i	0.409200	−	0.236252i
10.12	−0.316483	−	0.548164i	−2.25925	−	3.91313i	1.79968	−	3.11713i		−	2.41256i	−1.43003	+	2.47688i	2.84149	−	4.92160i	−4.81013			−5.70840	+	9.88723i	−1.32248	+	0.763533i
10.13	−0.164705	−	0.285277i	2.02430	+	3.50618i	1.94574	−	3.37013i			6.56611i	0.666822	−	1.15497i	−5.33997	+	9.24911i	−2.59953			−3.69555	+	6.40089i	1.87316	−	1.08147i
10.14	0.164705	+	0.285277i	2.02430	+	3.50618i	1.94574	−	3.37013i			6.56611i	−0.666822	+	1.15497i	5.33997	−	9.24911i	2.59953			−3.69555	+	6.40089i	−1.87316	+	1.08147i
10.15	0.316483	+	0.548164i	−2.25925	−	3.91313i	1.79968	−	3.11713i		−	2.41256i	1.43003	−	2.47688i	−2.84149	+	4.92160i	4.81013			−5.70840	+	9.88723i	1.32248	−	0.763533i
10.16	0.366250	+	0.634364i	−0.00402854	−	0.00697764i	1.73172	−	2.99943i			0.645057i	0.00295091	−	0.00511112i	−0.484629	+	0.839402i	5.46697			4.49997	−	7.79417i	−0.409200	+	0.236252i
10.17	0.635631	+	1.10094i	0.944665	+	1.63621i	1.19195	−	2.06451i		−	7.06986i	−1.20092	+	2.08005i	1.65995	−	2.87511i	8.11560			2.71522	−	4.70289i	7.78352	−	4.49382i
10.18	0.817329	+	1.41565i	−1.94998	−	3.37746i	0.663948	−	1.14999i			9.53698i	3.18754	−	5.52098i	4.86541	−	8.42713i	8.70928			−3.10481	+	5.37768i	−13.5011	+	7.79485i
10.19	0.880296	+	1.52472i	2.66253	+	4.61163i	0.450158	−	0.779697i		−	4.91448i	−4.68762	+	8.11920i	−4.54802	+	7.87741i	8.62746			−9.67810	+	16.7630i	7.49319	−	4.32620i
10.20	1.06551	+	1.84551i	−0.301239	−	0.521762i	−0.270613	+	0.468715i			4.58168i	0.641946	−	1.11188i	−5.32109	+	9.21640i	7.37070			4.31851	−	7.47988i	−8.45555	+	4.88181i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	inner
13.e	even	6	1	inner
143.i	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	143.3.i.a	✓	52
11.b	odd	2	1	inner	143.3.i.a	✓	52
13.e	even	6	1	inner	143.3.i.a	✓	52
143.i	odd	6	1	inner	143.3.i.a	✓	52

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
143.3.i.a	✓	52	1.a	even	1	1	trivial
143.3.i.a	✓	52	11.b	odd	2	1	inner
143.3.i.a	✓	52	13.e	even	6	1	inner
143.3.i.a	✓	52	143.i	odd	6	1	inner

Hecke kernels

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