Newform orbit 213.3.g.a

• Label: 213.3.g.a
• Level: $213$
• Weight: $3$
• Character orbit: 213.g
• Analytic conductor: $5.804$
• Analytic rank: $0$
• Dimension: $96$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 213 = 3 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	213.g (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.80382963087\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(24\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 96 q + 6 q^{2} - 66 q^{4} - 28 q^{8} - 72 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
46.1	−2.97771	+	2.16343i	1.40126	−	1.01807i	2.95025	−	9.07995i	1.15818	+	3.56452i	−1.97001	+	6.06306i	−2.74961	−	3.78452i	6.30932	+	19.4181i	0.927051	−	2.85317i	−11.1603	−	8.10845i
46.2	−2.93166	+	2.12997i	−1.40126	+	1.01807i	2.82176	−	8.68447i	1.22152	+	3.75946i	1.93954	−	5.96929i	0.561613	+	0.772993i	5.74610	+	17.6847i	0.927051	−	2.85317i	−11.5886	−	8.41963i
46.3	−2.63456	+	1.91412i	1.40126	−	1.01807i	2.04098	−	6.28150i	−1.91861	−	5.90488i	−1.74298	+	5.36435i	0.974649	+	1.34149i	2.62121	+	8.06724i	0.927051	−	2.85317i	16.3573	+	11.8843i
46.4	−2.15571	+	1.56621i	1.40126	−	1.01807i	0.957988	−	2.94838i	2.03264	+	6.25581i	−1.42618	+	4.38934i	6.11971	+	8.42306i	−0.740974	−	2.28048i	0.927051	−	2.85317i	−14.1797	−	10.3022i
46.5	−2.15562	+	1.56615i	−1.40126	+	1.01807i	0.957810	−	2.94784i	0.145193	+	0.446858i	1.42613	−	4.38917i	0.943839	+	1.29908i	−0.741417	−	2.28185i	0.927051	−	2.85317i	−1.01283	−	0.735863i
46.6	−1.92379	+	1.39772i	−1.40126	+	1.01807i	0.511296	−	1.57361i	−2.41811	−	7.44217i	1.27275	−	3.91712i	2.29845	+	3.16354i	−1.72346	−	5.30428i	0.927051	−	2.85317i	15.0540	+	10.9374i
46.7	−1.36835	+	0.994161i	1.40126	−	1.01807i	−0.352055	+	1.08351i	−0.118090	−	0.363445i	−0.905276	+	2.78615i	−3.09397	−	4.25848i	−2.68610	−	8.26697i	0.927051	−	2.85317i	0.522911	+	0.379917i
46.8	−1.13876	+	0.827360i	−1.40126	+	1.01807i	−0.623810	+	1.91989i	0.0828124	+	0.254870i	0.753389	−	2.31869i	−4.82258	−	6.63772i	−2.61794	−	8.05721i	0.927051	−	2.85317i	−0.305173	−	0.221722i
46.9	−0.822888	+	0.597863i	1.40126	−	1.01807i	−0.916364	+	2.82028i	−2.67601	−	8.23590i	−0.544410	+	1.67552i	6.56270	+	9.03279i	−2.18934	−	6.73808i	0.927051	−	2.85317i	7.12599	+	5.17733i
46.10	−0.666209	+	0.484029i	−1.40126	+	1.01807i	−1.02652	+	3.15930i	2.85333	+	8.78164i	0.440753	−	1.35650i	2.38698	+	3.28539i	−1.86319	−	5.73432i	0.927051	−	2.85317i	−6.15148	−	4.46931i
46.11	−0.531592	+	0.386224i	1.40126	−	1.01807i	−1.10265	+	3.39360i	0.182952	+	0.563069i	−0.351693	+	1.08240i	0.349929	+	0.481637i	−1.53673	−	4.72957i	0.927051	−	2.85317i	−0.314727	−	0.228662i
46.12	−0.172271	+	0.125163i	−1.40126	+	1.01807i	−1.22206	+	3.76110i	−0.408068	−	1.25590i	0.113972	−	0.350770i	8.11641	+	11.1713i	−0.523431	−	1.61096i	0.927051	−	2.85317i	0.227491	+	0.165282i
46.13	0.251872	−	0.182996i	−1.40126	+	1.01807i	−1.20612	+	3.71204i	−1.17127	−	3.60481i	−0.166635	+	0.512849i	−3.69104	−	5.08028i	0.760328	+	2.34005i	0.927051	−	2.85317i	−0.954677	−	0.693613i
46.14	0.814350	−	0.591660i	1.40126	−	1.01807i	−0.922964	+	2.84059i	−1.57264	−	4.84007i	0.538761	−	1.65814i	−7.31320	−	10.0658i	2.17326	+	6.68862i	0.927051	−	2.85317i	−4.14435	−	3.01105i
46.15	1.10336	−	0.801641i	−1.40126	+	1.01807i	−0.661284	+	2.03522i	0.904763	+	2.78457i	−0.729969	+	2.24661i	−5.64767	−	7.77336i	2.58767	+	7.96403i	0.927051	−	2.85317i	3.23051	+	2.34710i
46.16	1.31747	−	0.957198i	1.40126	−	1.01807i	−0.416569	+	1.28207i	0.735196	+	2.26270i	0.871618	−	2.68256i	5.40609	+	7.44084i	2.69129	+	8.28294i	0.927051	−	2.85317i	3.13445	+	2.27731i
46.17	1.32770	−	0.964633i	−1.40126	+	1.01807i	−0.403789	+	1.24273i	−1.61385	−	4.96692i	−0.878388	+	2.70340i	3.82793	+	5.26870i	2.69122	+	8.28272i	0.927051	−	2.85317i	−6.93397	−	5.03782i
46.18	1.47869	−	1.07433i	1.40126	−	1.01807i	−0.203728	+	0.627009i	2.74959	+	8.46237i	0.978280	−	3.01084i	−5.30254	−	7.29832i	2.63161	+	8.09925i	0.927051	−	2.85317i	13.1572	+	9.55927i
46.19	2.25005	−	1.63476i	−1.40126	+	1.01807i	1.15423	−	3.55234i	−2.41460	−	7.43137i	−1.48860	+	4.58143i	−0.818066	−	1.12597i	0.227621	+	0.700544i	0.927051	−	2.85317i	−17.5814	−	12.7737i
46.20	2.39107	−	1.73722i	−1.40126	+	1.01807i	1.46324	−	4.50340i	1.87527	+	5.77150i	−1.58190	+	4.86858i	3.77713	+	5.19877i	−0.671423	−	2.06643i	0.927051	−	2.85317i	14.5103	+	10.5423i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
71.e	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	213.3.g.a	✓	96
71.e	odd	10	1	inner	213.3.g.a	✓	96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
213.3.g.a	✓	96	1.a	even	1	1	trivial
213.3.g.a	✓	96	71.e	odd	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(213, [\chi])\).