Newform orbit 71.4.c.a

• Label: 71.4.c.a
• Level: $71$
• Weight: $4$
• Character orbit: 71.c
• Analytic conductor: $4.189$
• Analytic rank: $0$
• Dimension: $68$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	71.c (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.18913561041\)
Analytic rank:	\(0\)
Dimension:	\(68\)
Relative dimension:	\(17\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 68 q - 7 q^{3} - 82 q^{4} + 5 q^{5} + 58 q^{6} - 17 q^{7} + 15 q^{8} - 58 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1	−1.71834	−	5.28850i	1.25370	+	3.85850i	−18.5434	+	13.4726i	13.4058	+	9.73992i	18.2514	−	13.2604i	−3.26363	−	10.0444i	67.1244	+	48.7687i	8.52722	−	6.19539i	28.4738	−	87.6333i
5.2	−1.49365	−	4.59697i	−1.65291	−	5.08715i	−12.4290	+	9.03020i	−5.75362	−	4.18025i	−20.9166	+	15.1968i	4.34400	+	13.3695i	28.7928	+	20.9192i	−1.30346	+	0.947023i	−10.6226	+	32.6930i
5.3	−1.31990	−	4.06225i	2.65498	+	8.17119i	−8.28757	+	6.02128i	−14.2524	−	10.3550i	29.6891	−	21.5704i	10.2623	+	31.5842i	7.75428	+	5.63382i	−37.8760	+	27.5185i	−23.2526	+	71.5642i
5.4	−1.09752	−	3.37782i	1.23477	+	3.80024i	−3.73301	+	2.71219i	−2.82476	−	2.05231i	11.4813	−	8.34168i	−7.16162	−	22.0412i	−9.72844	−	7.06812i	8.92632	−	6.48535i	−3.83210	+	11.7940i
5.5	−1.04038	−	3.20196i	−1.71128	−	5.26678i	−2.69802	+	1.96023i	−1.06825	−	0.776132i	−15.0836	+	10.9589i	−5.37461	−	16.5414i	−12.7065	−	9.23179i	−2.96706	+	2.15570i	−1.37375	+	4.22798i
5.6	−0.807011	−	2.48372i	0.362971	+	1.11711i	0.954517	−	0.693497i	11.4545	+	8.32216i	2.48167	−	1.80304i	7.92653	+	24.3954i	−19.3950	−	14.0913i	20.7273	−	15.0592i	11.4261	−	35.1658i
5.7	−0.201436	−	0.619955i	−2.14262	−	6.59431i	6.12837	−	4.45252i	12.3676	+	8.98555i	−3.65658	+	2.65666i	−3.04582	−	9.37408i	−8.21375	−	5.96764i	−17.0507	+	12.3880i	3.07937	−	9.47734i
5.8	−0.155206	−	0.477676i	−2.77133	−	8.52929i	6.26805	−	4.55401i	−9.75945	−	7.09066i	−3.64411	+	2.64760i	6.70861	+	20.6470i	−6.39887	−	4.64905i	−43.2250	+	31.4048i	−1.87231	+	5.76237i
5.9	−0.136763	−	0.420915i	0.469118	+	1.44380i	6.31367	−	4.58715i	−14.5112	−	10.5430i	0.543557	−	0.394917i	−1.44821	−	4.45714i	−5.65869	−	4.11128i	19.9790	−	14.5156i	−2.45311	+	7.54989i
5.10	−0.0428156	−	0.131773i	2.44007	+	7.50977i	6.45661	−	4.69100i	5.27526	+	3.83270i	0.885110	−	0.643070i	−1.30921	−	4.02933i	−1.79133	−	1.30148i	−28.5992	+	20.7785i	0.279183	−	0.859236i
5.11	0.560170	+	1.72403i	−0.734226	−	2.25972i	3.81366	−	2.77079i	4.27497	+	3.10595i	3.48452	−	2.53165i	−7.99990	−	24.6212i	18.6456	+	13.5468i	17.2762	−	12.5519i	−2.96002	+	9.11002i
5.12	0.722923	+	2.22493i	−0.273673	−	0.842280i	2.04445	−	1.48538i	1.13828	+	0.827012i	1.67617	−	1.21781i	7.17951	+	22.0963i	19.9239	+	14.4756i	21.2089	−	15.4092i	−1.01715	+	3.13047i
5.13	1.10746	+	3.40842i	2.31368	+	7.12078i	−3.91872	+	2.84712i	−6.64995	−	4.83147i	−21.7083	+	15.7720i	3.37484	+	10.3867i	9.15100	+	6.64859i	−23.5089	+	17.0802i	9.10311	−	28.0165i
5.14	1.21405	+	3.73646i	−2.03366	−	6.25895i	−6.01506	+	4.37020i	−11.8378	−	8.60064i	20.9173	−	15.1973i	−5.66052	−	17.4213i	1.79573	+	1.30467i	−13.1953	+	9.58692i	17.7643	−	54.6729i
5.15	1.33457	+	4.10739i	1.44267	+	4.44009i	−8.61741	+	6.26091i	15.1975	+	11.0416i	−16.3118	+	11.8512i	−7.66305	−	23.5844i	−9.26492	−	6.73136i	4.21035	−	3.05900i	−25.0700	+	77.1576i
5.16	1.40657	+	4.32897i	−2.57172	−	7.91494i	−10.2894	+	7.47572i	14.2129	+	10.3263i	30.6463	−	22.2658i	6.15873	+	18.9546i	−17.3754	−	12.6240i	−34.1891	+	24.8398i	−24.7108	+	76.0521i
5.17	1.66728	+	5.13135i	0.528475	+	1.62648i	−17.0788	+	12.4085i	−5.50629	−	4.00055i	−7.46493	+	5.42359i	1.10726	+	3.40778i	−57.2277	−	41.5783i	19.4773	−	14.1511i	11.3477	−	34.9247i
25.1	−4.07184	+	2.95836i	1.47610	−	1.07245i	5.35582	−	16.4835i	3.09531	+	9.52637i	−2.83775	+	8.73369i	−9.98363	+	7.25353i	14.5138	+	44.6688i	−7.31473	+	22.5124i	−40.7861	−	29.6328i
25.2	−4.03587	+	2.93223i	−7.64447	+	5.55403i	5.21814	−	16.0598i	−2.73636	−	8.42166i	14.5664	−	44.8307i	−19.3464	+	14.0560i	13.6987	+	42.1604i	19.2471	−	59.2366i	35.7379	+	25.9651i
25.3	−3.30302	+	2.39979i	−1.21333	+	0.881536i	2.67885	−	8.24466i	−2.24798	−	6.91858i	1.89216	−	5.82347i	18.3511	−	13.3328i	0.843979	+	2.59750i	−7.64839	+	23.5393i	24.0283	+	17.4575i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
71.c	even	5	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	71.4.c.a	✓	68
71.c	even	5	1	inner	71.4.c.a	✓	68

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
71.4.c.a	✓	68	1.a	even	1	1	trivial
71.4.c.a	✓	68	71.c	even	5	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(71, [\chi])\).