Newform orbit 211.3.g.a

• Label: 211.3.g.a
• Level: $211$
• Weight: $3$
• Character orbit: 211.g
• Analytic conductor: $5.749$
• Analytic rank: $0$
• Dimension: $140$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	211.g (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.74933357800\)
Analytic rank:	\(0\)
Dimension:	\(140\)
Relative dimension:	\(35\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 140 q - 5 q^{2} + 5 q^{3} + 67 q^{4} - 3 q^{5} + 15 q^{6} + 20 q^{7} + 20 q^{8} + 126 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
23.1	−3.73368	−	1.21315i	−3.22547	−	4.43947i	9.23258	+	6.70786i	5.29877	+	3.84978i	6.65713	+	20.4885i	3.90220	−	1.26790i	−17.1037	−	23.5413i	−6.52414	+	20.0792i	−15.1136	−	20.8020i
23.2	−3.54385	−	1.15147i	0.412714	+	0.568052i	7.99693	+	5.81011i	0.806112	+	0.585674i	−0.808503	−	2.48832i	−11.6429	+	3.78300i	−12.8889	−	17.7401i	2.62880	−	8.09062i	−2.18235	−	3.00375i
23.3	−3.38237	−	1.09900i	−0.807471	−	1.11139i	6.99658	+	5.08331i	−7.27913	−	5.28860i	1.50975	+	4.64654i	8.69138	−	2.82400i	−9.71680	−	13.3740i	2.19798	−	6.76468i	18.8086	+	25.8878i
23.4	−3.32441	−	1.08017i	1.33939	+	1.84351i	6.64886	+	4.83068i	2.37931	+	1.72867i	−2.46137	−	7.57533i	3.89791	−	1.26651i	−8.66720	−	11.9294i	1.17659	−	3.62117i	−6.04255	−	8.31685i
23.5	−3.05186	−	0.991610i	2.74827	+	3.78267i	5.09451	+	3.70138i	−4.85305	−	3.52594i	−4.63641	−	14.2694i	−0.268925	+	0.0873791i	−4.33279	−	5.96358i	−3.97445	+	12.2321i	11.3145	+	15.5730i
23.6	−2.74536	−	0.892021i	−0.982107	−	1.35175i	3.50522	+	2.54669i	0.835284	+	0.606869i	1.49044	+	4.58711i	−0.531978	+	0.172850i	−0.564479	−	0.776939i	1.91845	−	5.90437i	−1.75181	−	2.41116i
23.7	−2.70904	−	0.880221i	1.59206	+	2.19128i	3.32805	+	2.41797i	7.38604	+	5.36627i	−2.38414	−	7.33763i	9.90697	−	3.21897i	−0.190360	−	0.262009i	0.514096	−	1.58223i	−15.2856	−	21.0388i
23.8	−2.55354	−	0.829696i	−2.78185	−	3.82889i	2.59611	+	1.88618i	−4.75442	−	3.45429i	3.92676	+	12.0853i	−9.56586	+	3.10813i	1.24839	+	1.71827i	−4.14054	+	12.7433i	9.27460	+	12.7654i
23.9	−2.48846	−	0.808549i	−2.01984	−	2.78007i	2.30260	+	1.67294i	0.634798	+	0.461208i	2.77847	+	8.55124i	3.95184	−	1.28403i	1.77453	+	2.44244i	−0.867899	+	2.67112i	−1.20676	−	1.66096i
23.10	−2.05888	−	0.668971i	3.14755	+	4.33224i	0.555399	+	0.403521i	5.04396	+	3.66465i	−3.58230	−	11.0252i	−11.5212	+	3.74345i	4.21628	+	5.80321i	−6.08002	+	18.7124i	−7.93336	−	10.9193i
23.11	−1.83496	−	0.596213i	1.94828	+	2.68157i	−0.224475	−	0.163091i	−3.04665	−	2.21352i	−1.97621	−	6.08216i	3.21406	−	1.04431i	4.85093	+	6.67673i	−0.613903	+	1.88940i	4.27073	+	5.87816i
23.12	−1.50965	−	0.490515i	0.124162	+	0.170895i	−1.19763	−	0.870129i	1.95505	+	1.42043i	−0.103615	−	0.318895i	−3.07846	+	1.00025i	5.11325	+	7.03779i	2.76736	−	8.51707i	−2.25470	−	3.10333i
23.13	−1.14727	−	0.372772i	0.350983	+	0.483087i	−2.05879	−	1.49580i	−4.88353	−	3.54809i	−0.222593	−	0.685070i	−9.20889	+	2.99215i	4.64062	+	6.38727i	2.67097	−	8.22040i	4.28012	+	5.89108i
23.14	−0.968664	−	0.314738i	−2.77286	−	3.81651i	−2.39682	−	1.74139i	5.95971	+	4.32998i	1.48477	+	4.56965i	−8.23950	+	2.67718i	4.16830	+	5.73717i	−4.09588	+	12.6058i	−4.41015	−	6.07004i
23.15	−0.784203	−	0.254803i	−0.953717	−	1.31268i	−2.68602	−	1.95151i	−6.22377	−	4.52183i	0.413433	+	1.27242i	7.28185	−	2.36602i	3.54779	+	4.88311i	1.96760	−	6.05566i	3.72852	+	5.13187i
23.16	−0.765864	−	0.248844i	−2.01231	−	2.76971i	−2.71144	−	1.96998i	4.21978	+	3.06585i	0.851930	+	2.62197i	11.9634	−	3.88714i	3.47970	+	4.78939i	−0.840737	+	2.58752i	−2.46886	−	3.39809i
23.17	−0.371567	−	0.120729i	2.99203	+	4.11818i	−3.11258	−	2.26142i	0.366386	+	0.266195i	−0.614555	−	1.89141i	10.6839	−	3.47142i	1.80208	+	2.48035i	−5.22598	+	16.0839i	−0.103999	−	0.143143i
23.18	−0.218254	−	0.0709151i	−2.35318	−	3.23888i	−3.19346	−	2.32019i	−4.96982	−	3.61079i	0.283907	+	0.873776i	0.168081	−	0.0546130i	1.07200	+	1.47549i	−2.17172	+	6.68386i	0.828625	+	1.14050i
23.19	−0.132651	−	0.0431009i	0.929835	+	1.27981i	−3.22033	−	2.33971i	5.75033	+	4.17786i	−0.0681826	−	0.209845i	−1.25443	+	0.407588i	0.654267	+	0.900522i	2.00784	−	6.17949i	−0.582717	−	0.802042i
23.20	0.498622	+	0.162012i	2.35399	+	3.23999i	−3.01369	−	2.18958i	−3.27074	−	2.37633i	0.648832	+	1.99690i	−9.41044	+	3.05764i	−2.38061	−	3.27664i	−2.17510	+	6.69427i	−1.24587	−	1.71479i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
211.g	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	211.3.g.a	✓	140
211.g	odd	10	1	inner	211.3.g.a	✓	140

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
211.3.g.a	✓	140	1.a	even	1	1	trivial
211.3.g.a	✓	140	211.g	odd	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(211, [\chi])\).