Newform orbit 289.3.j.a

• Label: 289.3.j.a
• Level: $289$
• Weight: $3$
• Character orbit: 289.j
• Analytic conductor: $7.875$
• Analytic rank: $0$
• Dimension: $6400$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	289.j (of order \(272\), degree \(128\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.87467964001\)
Analytic rank:	\(0\)
Dimension:	\(6400\)
Relative dimension:	\(50\) over \(\Q(\zeta_{272})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{272}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 6400 q - 128 q^{2} - 128 q^{3} - 128 q^{4} - 128 q^{5} - 128 q^{6} - 128 q^{7} - 128 q^{8} - 128 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−2.19866	+	3.05578i	5.58918	+	0.0645578i	−3.23254	−	9.64458i	0.303425	−	0.164444i	−12.4860	+	16.9374i	−1.47029	+	6.59201i	22.1946	+	6.87287i	22.2372	+	0.513769i	−0.164623	+	1.28876i
3.2	−2.18546	+	3.03745i	−0.584274	−	0.00674865i	−3.17866	−	9.48382i	−7.01523	+	3.80197i	1.29741	−	1.75995i	−1.51640	+	6.79874i	21.4554	+	6.64396i	−8.65627	−	0.199995i	3.78326	−	29.6174i
3.3	−2.13252	+	2.96387i	0.594430	+	0.00686595i	−2.96568	−	8.84839i	8.45919	−	4.58454i	−1.28799	+	1.74717i	−0.230994	+	1.03566i	18.5982	+	5.75918i	−8.64430	−	0.199718i	−4.45148	+	34.8486i
3.4	−2.12889	+	2.95881i	−3.90905	−	0.0451515i	−2.95125	−	8.80532i	0.502256	−	0.272202i	8.45553	−	11.4700i	−0.985652	+	4.41914i	18.4083	+	5.70039i	6.28106	+	0.145118i	−0.263851	+	2.06557i
3.5	−2.09965	+	2.91818i	−4.19923	−	0.0485032i	−2.83606	−	8.46165i	2.00062	−	1.08425i	8.95846	−	12.1523i	2.92376	−	13.1086i	16.9107	+	5.23665i	8.63361	+	0.199471i	−1.03656	+	8.11472i
3.6	−2.04464	+	2.84172i	2.03957	+	0.0235580i	−2.62367	−	7.82796i	0.704208	−	0.381652i	−4.23712	+	5.74771i	0.731436	−	3.27937i	14.2326	+	4.40734i	−4.83833	−	0.111785i	−0.355303	+	2.78150i
3.7	−1.85242	+	2.57456i	3.40348	+	0.0393118i	−1.92575	−	5.74567i	−6.33689	+	3.43434i	−6.40586	+	8.68963i	1.90659	−	8.54812i	6.24075	+	1.93254i	2.58450	+	0.0597125i	2.89665	−	22.6765i
3.8	−1.70290	+	2.36676i	−2.76682	−	0.0319581i	−1.43051	−	4.26806i	−2.94217	+	1.59454i	4.78725	−	6.49396i	−0.0565029	+	0.253329i	1.39654	+	0.432457i	−1.34335	−	0.0310367i	1.23634	−	9.67875i
3.9	−1.68133	+	2.33678i	3.66300	+	0.0423094i	−1.36250	−	4.06514i	3.94321	−	2.13706i	−6.25757	+	8.48847i	1.65124	−	7.40328i	0.790311	+	0.244731i	4.41816	+	0.102078i	−1.63600	+	12.8075i
3.10	−1.56213	+	2.17110i	−0.836789	−	0.00966533i	−1.00229	−	2.99043i	4.41869	−	2.39475i	1.32815	−	1.80166i	−0.0540467	+	0.242317i	−2.16170	−	0.669402i	−8.29748	−	0.191705i	−1.70330	+	13.3343i
3.11	−1.51459	+	2.10503i	2.06357	+	0.0238353i	−0.866024	−	2.58386i	−3.31190	+	1.79491i	−3.17564	+	4.30779i	−1.77432	+	7.95511i	−3.15814	−	0.977964i	−4.73983	−	0.109509i	1.23780	−	9.69020i
3.12	−1.46004	+	2.02922i	−4.57820	−	0.0528805i	−0.714857	−	2.13284i	5.81707	−	3.15262i	6.79167	−	9.21298i	−2.58339	+	11.5825i	−4.18033	−	1.29450i	11.9596	+	0.276314i	−2.09580	+	16.4071i
3.13	−1.37549	+	1.91171i	−1.96360	−	0.0226805i	−0.491498	−	1.46643i	−7.15221	+	3.87621i	2.74427	−	3.72264i	2.45510	−	11.0074i	−5.51947	−	1.70918i	−5.14239	−	0.118810i	2.42761	−	19.0046i
3.14	−1.20606	+	1.67623i	3.04858	+	0.0352126i	−0.0839933	−	0.250602i	0.433583	−	0.234984i	−3.73578	+	5.06764i	−2.82560	+	12.6685i	−7.36905	−	2.28193i	0.295001	+	0.00681572i	−0.129039	+	1.01019i
3.15	−1.16092	+	1.61349i	−5.73467	−	0.0662382i	0.0155425	+	0.0463726i	−1.16506	+	0.631413i	6.76437	−	9.17595i	0.817329	−	3.66447i	−7.68799	−	2.38069i	23.8845	+	0.551828i	0.333757	−	2.61283i
3.16	−0.997213	+	1.38597i	4.86454	+	0.0561878i	0.344698	+	1.02844i	8.37418	−	4.53846i	−4.92885	+	6.68605i	−0.941092	+	4.21936i	−8.29321	−	2.56811i	14.6630	+	0.338774i	−2.06068	+	16.1321i
3.17	−0.924339	+	1.28468i	−0.0772130		0.000891848i	0.475158	+	1.41768i	3.02256	−	1.63810i	0.0725167	−	0.0983699i	0.678506	−	3.04206i	−8.30780	−	2.57263i	−8.99164	−	0.207743i	−0.689426	+	5.39720i
3.18	−0.844489	+	1.17370i	5.69142	+	0.0657387i	0.606746	+	1.81028i	−5.95260	+	3.22607i	−4.88350	+	6.62453i	−0.264765	+	1.18707i	−8.16205	−	2.52750i	23.3903	+	0.540412i	1.24046	−	9.71097i
3.19	−0.790275	+	1.09836i	−3.63560	−	0.0419929i	0.689316	+	2.05664i	−5.89038	+	3.19235i	2.91925	−	3.95999i	−1.45872	+	6.54014i	−7.97391	−	2.46923i	4.21822	+	0.0974581i	1.14869	−	8.99256i
3.20	−0.713016	+	0.990978i	−1.29507	−	0.0149587i	0.797520	+	2.37948i	2.20997	−	1.19771i	0.938231	−	1.27272i	1.59500	−	7.15113i	−7.59144	−	2.35080i	−7.32061	−	0.169136i	−0.388836	+	3.04402i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
289.j	odd	272	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	289.3.j.a	✓	6400
289.j	odd	272	1	inner	289.3.j.a	✓	6400

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
289.3.j.a	✓	6400	1.a	even	1	1	trivial
289.3.j.a	✓	6400	289.j	odd	272	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(289, [\chi])\).