Newform orbit 89.4.e.a

• Label: 89.4.e.a
• Level: $89$
• Weight: $4$
• Character orbit: 89.e
• Analytic conductor: $5.251$
• Analytic rank: $0$
• Dimension: $220$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 89 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	89.e (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.25116999051\)
Analytic rank:	\(0\)
Dimension:	\(220\)
Relative dimension:	\(22\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 220 q - 9 q^{2} + 11 q^{3} - 97 q^{4} - 3 q^{5} + 19 q^{6} - 9 q^{7} + 7 q^{8} - 353 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−5.36479	+	1.57525i	1.44262	+	0.927115i	19.5696	−	12.5766i	6.90497	−	7.96876i	−9.19979	−	2.70130i	−8.04215	+	9.28113i	−55.8835	+	64.4930i	−9.99460	−	21.8851i	−24.4910	+	53.6278i
2.2	−4.66735	+	1.37046i	−5.81558	−	3.73745i	13.1760	−	8.46768i	−2.58411	+	2.98222i	32.2654	+	9.47397i	20.0671	−	23.1586i	−24.4083	+	28.1686i	8.63629	+	18.9108i	7.97393	−	17.4605i
2.3	−4.33371	+	1.27249i	6.72764	+	4.32359i	10.4318	−	6.70411i	−10.3845	+	11.9843i	−34.6574	−	10.1763i	−3.64551	+	4.20715i	−13.0152	+	15.0203i	15.3515	+	33.6151i	29.7534	−	65.1507i
2.4	−3.76121	+	1.10439i	−5.42699	−	3.48772i	6.19699	−	3.98257i	−12.1584	+	14.0315i	24.2639	+	7.12451i	−20.5322	+	23.6955i	1.62654	−	1.87712i	6.07187	+	13.2955i	30.2339	−	66.2030i
2.5	−3.70535	+	1.08799i	0.265891	+	0.170878i	5.81589	−	3.73765i	0.516177	−	0.595700i	−1.17113	−	0.343875i	−1.05233	+	1.21445i	2.74803	−	3.17139i	−11.1747	−	24.4692i	−1.26450	+	2.76887i
2.6	−3.39189	+	0.995949i	6.39803	+	4.11176i	3.78298	−	2.43117i	7.29177	−	8.41515i	−25.7965	−	7.57454i	19.4533	−	22.4503i	8.10979	−	9.35919i	12.8120	+	28.0543i	−16.3518	+	35.8055i
2.7	−3.14586	+	0.923709i	−6.04601	−	3.88554i	2.31319	−	1.48660i	14.3974	−	16.6155i	22.6090	+	6.63861i	−8.96851	+	10.3502i	11.2728	−	13.0095i	10.2407	+	22.4240i	−29.9445	+	65.5693i
2.8	−1.78480	+	0.524065i	0.822551	+	0.528621i	−3.81916	+	2.45442i	0.633944	−	0.731610i	−1.74512	−	0.512414i	−7.25606	+	8.37394i	15.2753	−	17.6286i	−10.8191	−	23.6904i	−0.748052	+	1.63801i
2.9	−1.35520	+	0.397924i	0.766340	+	0.492497i	−5.05179	+	3.24659i	−12.8289	+	14.8053i	−1.23452	−	0.362489i	20.4502	−	23.6008i	12.9538	−	14.9495i	−10.8715	−	23.8052i	11.4944	−	25.1692i
2.10	−0.842904	+	0.247499i	6.66287	+	4.28197i	−6.08080	+	3.90789i	−0.0585026	+	0.0675156i	−6.67595	−	1.96023i	−18.3005	+	21.1199i	8.76063	−	10.1103i	14.8424	+	32.5004i	0.0326021	−	0.0713885i
2.11	−0.736589	+	0.216282i	−6.63566	−	4.26448i	−6.23424	+	4.00650i	−1.47406	+	1.70116i	5.81008	+	1.70599i	5.22135	−	6.02576i	7.74736	−	8.94093i	14.6300	+	32.0351i	0.717848	−	1.57187i
2.12	−0.0519233	+	0.0152460i	3.14162	+	2.01900i	−6.72756	+	4.32354i	13.4494	−	15.5214i	−0.193905	−	0.0569356i	7.22556	−	8.33874i	0.566904	−	0.654242i	−5.42277	−	11.8742i	−0.461695	+	1.01097i
2.13	1.16704	−	0.342673i	−2.35024	−	1.51041i	−5.48547	+	3.52530i	6.55587	−	7.56588i	−3.26039	−	0.957338i	9.34504	−	10.7847i	−11.5658	+	13.3477i	−7.97391	−	17.4604i	5.05833	−	11.0762i
2.14	1.22703	−	0.360287i	7.52571	+	4.83648i	−5.35424	+	3.44096i	−3.93189	+	4.53764i	10.9768	+	3.22307i	13.8445	−	15.9774i	−12.0297	+	13.8830i	22.0286	+	48.2358i	−3.18967	+	6.98440i
2.15	1.91474	−	0.562219i	0.771590	+	0.495871i	−3.37989	+	2.17212i	−9.68936	+	11.1821i	1.75618	+	0.515662i	−8.62785	+	9.95707i	−15.7050	+	18.1245i	−10.8667	−	23.7948i	−12.2658	+	26.8584i
2.16	2.12186	−	0.623034i	−4.89743	−	3.14739i	−2.61592	+	1.68115i	2.83234	−	3.26869i	−12.3526	−	3.62704i	−19.1774	+	22.1319i	−16.0887	+	18.5673i	2.86257	+	6.26816i	3.97331	−	8.70034i
2.17	3.57191	−	1.04881i	4.83240	+	3.10559i	4.92848	−	3.16734i	11.5690	−	13.3513i	20.5180	+	6.02464i	−14.1513	+	16.3315i	−5.22065	+	6.02496i	2.49116	+	5.45489i	27.3203	−	59.8231i
2.18	3.59249	−	1.05485i	−7.73809	−	4.97297i	5.06324	−	3.25395i	−12.3227	+	14.2212i	−33.0447	−	9.70281i	7.00997	−	8.08993i	−4.85798	+	5.60640i	23.9314	+	52.4025i	−29.2681	+	64.0882i
2.19	3.69849	−	1.08598i	5.70446	+	3.66603i	5.76948	−	3.70782i	−1.86069	+	2.14735i	25.0791	+	7.36389i	6.96785	−	8.04133i	−2.88219	+	3.32623i	7.88484	+	17.2654i	−4.54979	+	9.96264i
2.20	3.93257	−	1.15471i	−2.18714	−	1.40559i	7.40171	−	4.75679i	3.39944	−	3.92316i	−10.2241	−	3.00207i	17.2418	−	19.8981i	2.14299	−	2.47314i	−8.40831	−	18.4116i	8.83843	−	19.3535i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
89.e	even	11	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	89.4.e.a	✓	220
89.e	even	11	1	inner	89.4.e.a	✓	220

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
89.4.e.a	✓	220	1.a	even	1	1	trivial
89.4.e.a	✓	220	89.e	even	11	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(89, [\chi])\).