Newform orbit 229.3.l.a

• Label: 229.3.l.a
• Level: $229$
• Weight: $3$
• Character orbit: 229.l
• Analytic conductor: $6.240$
• Analytic rank: $0$
• Dimension: $2664$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 229 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	229.l (of order \(228\), degree \(72\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.23979805385\)
Analytic rank:	\(0\)
Dimension:	\(2664\)
Relative dimension:	\(37\) over \(\Q(\zeta_{228})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{228}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 2664 q - 76 q^{2} - 74 q^{3} - 76 q^{4} - 52 q^{5} - 76 q^{6} - 56 q^{7} - 64 q^{8} + 140 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
6.1	−3.72752	−	1.10973i	−0.567277	+	0.160411i	9.31426	+	6.08531i	0.543785	+	2.42647i	2.29255	+	0.0315909i	−0.673163	−	6.95757i	−17.9117	−	21.1483i	−7.37120	+	4.53106i	0.665761	−	9.64819i
6.2	−3.62784	−	1.08005i	5.04384	−	1.42626i	8.64604	+	5.64874i	0.151846	+	0.677564i	−19.8387	−	0.273373i	0.568654	+	5.87740i	−15.4800	−	18.2772i	15.7388	−	9.67463i	0.180934	−	2.62209i
6.3	−3.57938	−	1.06563i	−3.69217	+	1.04405i	8.32772	+	5.44077i	−1.32294	−	5.90320i	14.3282	+	0.197440i	0.150613	+	1.55668i	−14.3555	−	16.9495i	4.87482	−	2.99654i	−1.55531	+	22.5396i
6.4	−3.08962	−	0.919819i	2.40893	−	0.681180i	5.35101	+	3.49599i	−1.24878	−	5.57229i	−8.06924	−	0.111192i	−0.941809	−	9.73420i	−4.98318	−	5.88363i	−2.32834	+	1.43123i	−1.26725	+	18.3649i
6.5	−3.07282	−	0.914819i	0.628472	−	0.177715i	5.25668	+	3.43436i	1.43683	+	6.41141i	−2.09376	−	0.0288516i	0.519403	+	5.36837i	−4.72260	−	5.57596i	−7.30388	+	4.48968i	1.45015	−	21.0156i
6.6	−3.01961	−	0.898977i	−4.37606	+	1.23743i	4.96123	+	3.24133i	0.815502	+	3.63892i	14.3264	+	0.197415i	0.476069	+	4.92047i	−3.92220	−	4.63093i	9.95142	−	6.11711i	0.808811	−	11.7213i
6.7	−2.72858	−	0.812333i	1.91015	−	0.540139i	3.43659	+	2.24523i	−1.41945	−	6.33385i	−5.65077	−	0.0778664i	1.11371	+	11.5109i	−0.193240	−	0.228158i	−4.31035	+	2.64956i	−1.27212	+	18.4355i
6.8	−2.31804	−	0.690110i	4.73612	−	1.33925i	1.54839	+	1.01161i	1.97073	+	8.79379i	−11.9027	−	0.164017i	−0.581402	−	6.00916i	3.36142	+	3.96883i	12.9700	−	7.97264i	1.50044	−	21.7444i
6.9	−2.24201	−	0.667475i	−2.15777	+	0.610159i	1.23241	+	0.805174i	−0.400132	−	1.78547i	5.24500	+	0.0722750i	0.167487	+	1.73108i	3.82180	+	4.51239i	−3.38361	+	2.07989i	−0.294654	+	4.27011i
6.10	−2.15287	−	0.640938i	−5.28862	+	1.49548i	0.875390	+	0.571921i	−1.17289	−	5.23365i	12.3442	+	0.170101i	−0.886470	−	9.16223i	4.28897	+	5.06398i	18.0657	−	11.1050i	−0.829366	+	12.0191i
6.11	−2.13033	−	0.634226i	−1.26115	+	0.356619i	0.787393	+	0.514430i	0.860820	+	3.84114i	2.91284	+	0.0401384i	−1.23906	−	12.8065i	4.39506	+	5.18924i	−6.20395	+	3.81356i	0.602324	−	8.72886i
6.12	−1.77711	−	0.529069i	3.31393	−	0.937090i	−0.470451	−	0.307361i	0.00422374	+	0.0188471i	−6.38501	−	0.0879841i	−0.194866	−	2.01407i	5.46689	+	6.45475i	2.43672	−	1.49785i	0.00246537	−	0.0357281i
6.13	−1.10212	−	0.328116i	−4.53997	+	1.28378i	−2.24165	−	1.46455i	2.07852	+	9.27476i	5.42482	+	0.0747529i	0.204388	+	2.11248i	4.96282	+	5.85959i	11.2959	−	6.94359i	0.752411	−	10.9039i
6.14	−1.04363	−	0.310701i	2.98694	−	0.844626i	−2.35605	−	1.53928i	0.606652	+	2.70700i	−3.37967	−	0.0465712i	0.722293	+	7.46536i	4.79558	+	5.66213i	0.541139	−	0.332637i	0.207948	−	3.01358i
6.15	−1.03336	−	0.307646i	5.63555	−	1.59358i	−2.37547	−	1.55197i	−1.67168	−	7.45936i	−6.31383	−	0.0870032i	−0.0499500	−	0.516265i	4.76459	+	5.62554i	21.5527	−	13.2484i	−0.567385	+	8.22252i
6.16	−0.842385	−	0.250789i	−1.16507	+	0.329450i	−2.70195	−	1.76527i	−1.95052	−	8.70358i	1.06406	+	0.0146625i	−0.222006	−	2.29458i	4.10556	+	4.84743i	−6.41843	+	3.94539i	−0.539674	+	7.82093i
6.17	−0.716194	−	0.213220i	−3.07874	+	0.870585i	−2.88120	−	1.88238i	−0.184636	−	0.823882i	2.39060	+	0.0329420i	1.34392	+	13.8903i	3.59394	+	4.24336i	1.05346	−	0.647557i	−0.0434329	+	0.629428i
6.18	−0.398037	−	0.118501i	1.04474	−	0.295423i	−3.20428	−	2.09346i	0.564885	+	2.52062i	−0.450851	−	0.00621263i	0.293205	+	3.03046i	2.10098	+	2.48062i	−6.66308	+	4.09578i	0.0738506	−	1.07024i
6.19	−0.240987	−	0.0717449i	−1.34641	+	0.380727i	−3.29574	−	2.15321i	1.55562	+	6.94147i	0.351781	+	0.00484747i	−0.565379	−	5.84355i	1.28977	+	1.52283i	−5.99942	+	3.68783i	0.123131	−	1.78441i
6.20	0.161729	+	0.0481487i	1.53092	−	0.432902i	−3.32483	−	2.17222i	−0.230250	−	1.02742i	0.268437	+	0.00369900i	−1.12397	−	11.6169i	−0.869366	−	1.02646i	−5.51097	+	3.38758i	0.0122309	−	0.177249i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
229.l	odd	228	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	229.3.l.a	✓	2664
229.l	odd	228	1	inner	229.3.l.a	✓	2664

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
229.3.l.a	✓	2664	1.a	even	1	1	trivial
229.3.l.a	✓	2664	229.l	odd	228	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(229, [\chi])\).