Newform orbit 592.2.bj.a

• Label: 592.2.bj.a
• Level: $592$
• Weight: $2$
• Character orbit: 592.bj
• Analytic conductor: $4.727$
• Analytic rank: $0$
• Dimension: $296$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bj (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.72714379966\)
Analytic rank:	\(0\)
Dimension:	\(296\)
Relative dimension:	\(74\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 296 q - 2 q^{2} - 2 q^{3} - 2 q^{5} - 8 q^{6} - 8 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
269.1	−1.41095	+	0.0959738i	−0.423008	+	1.57869i	1.98158	−	0.270829i	1.66707	+	0.446689i	0.445332	−	2.26805i	1.50872	−	0.871059i	−2.76992	+	0.572307i	0.284754	+	0.164403i	−2.39502	−	0.470263i
269.2	−1.39545	−	0.229610i	−0.0391316	+	0.146041i	1.89456	+	0.640818i	−0.838221	−	0.224601i	0.0881387	−	0.194808i	4.06643	−	2.34775i	−2.49662	−	1.32924i	2.57828	+	1.48857i	1.11812	+	0.505883i
269.3	−1.39384	+	0.239180i	0.716954	−	2.67571i	1.88559	−	0.666758i	0.464886	+	0.124566i	−0.359344	+	3.90100i	2.33937	−	1.35063i	−2.46873	+	1.38035i	−4.04732	−	2.33672i	−0.677771	−	0.0624335i
269.4	−1.38840	−	0.268987i	0.418183	−	1.56068i	1.85529	+	0.746921i	3.88437	+	1.04081i	−1.00041	+	2.05436i	−0.987385	+	0.570067i	−2.37497	−	1.53607i	0.337235	+	0.194703i	−5.11308	−	2.48990i
269.5	−1.38740	+	0.274090i	−0.734493	+	2.74116i	1.84975	−	0.760543i	−3.74078	−	1.00234i	0.267709	−	4.00440i	−1.19382	+	0.689255i	−2.35788	+	1.56217i	−4.37642	−	2.52673i	5.46469	+	0.365335i
269.6	−1.37864	+	0.315183i	0.0791195	−	0.295278i	1.80132	−	0.869050i	−0.990006	−	0.265271i	−0.0160111	+	0.432021i	−2.93859	+	1.69660i	−2.20947	+	1.76586i	2.51715	+	1.45328i	1.44847	+	0.0536817i
269.7	−1.36904	−	0.354576i	0.282059	−	1.05266i	1.74855	+	0.970860i	−3.85830	−	1.03383i	−0.759398	+	1.34112i	0.920818	−	0.531634i	−2.04960	−	1.94914i	1.56955	+	0.906178i	4.91560	+	2.78342i
269.8	−1.36628	−	0.365072i	−0.237302	+	0.885623i	1.73344	+	0.997582i	−1.86160	−	0.498814i	0.647537	−	1.12338i	−2.00917	+	1.16000i	−2.00418	−	1.99581i	1.87006	+	1.07968i	2.36136	+	1.36114i
269.9	−1.34304	−	0.442979i	−0.563706	+	2.10378i	1.60754	+	1.18988i	2.24529	+	0.601624i	1.68901	−	2.57576i	−1.51732	+	0.876025i	−1.63191	−	2.31017i	−1.51005	−	0.871826i	−2.74902	−	1.80262i
269.10	−1.32597	+	0.491728i	0.333408	−	1.24429i	1.51641	−	1.30404i	0.195429	+	0.0523650i	0.169766	+	1.81385i	−2.32311	+	1.34125i	−1.36948	+	2.47478i	1.16097	+	0.670286i	−0.284883	+	0.0266634i
269.11	−1.30794	+	0.537854i	−0.762904	+	2.84720i	1.42143	−	1.40696i	2.34044	+	0.627119i	−0.533541	−	4.13430i	1.29597	−	0.748229i	−1.10240	+	2.60475i	−4.92644	−	2.84428i	−3.39846	+	0.438579i
269.12	−1.29531	−	0.567601i	0.811348	−	3.02799i	1.35566	+	1.47044i	0.0502312	+	0.0134594i	−2.76964	+	3.46167i	−1.61246	+	0.930956i	−0.921373	−	2.67415i	−5.91237	−	3.41351i	−0.0574255	−	0.0459454i
269.13	−1.16782	−	0.797612i	−0.730399	+	2.72589i	0.727629	+	1.86294i	−1.69065	−	0.453007i	3.02718	−	2.60078i	0.695613	−	0.401612i	0.636164	−	2.75596i	−4.29890	−	2.48197i	1.61305	+	1.87751i
269.14	−1.16448	+	0.802488i	0.0890257	−	0.332248i	0.712027	−	1.86896i	3.30786	+	0.886338i	0.162957	+	0.458339i	3.04766	−	1.75957i	0.670678	+	2.74776i	2.49561	+	1.44084i	−4.56321	+	1.62239i
269.15	−1.15637	+	0.814134i	0.345577	−	1.28971i	0.674371	−	1.88288i	−3.28600	−	0.880481i	0.650384	+	1.77273i	2.78237	−	1.60640i	0.753094	+	2.72633i	1.05414	+	0.608610i	4.51665	−	1.65709i
269.16	−1.09328	−	0.897071i	0.323137	−	1.20596i	0.390528	+	1.96150i	0.304513	+	0.0815940i	−1.43511	+	1.02858i	−3.83002	+	2.21126i	1.33265	−	2.49480i	1.24815	+	0.720618i	−0.259723	−	0.362375i
269.17	−1.05177	−	0.945403i	0.0493774	−	0.184279i	0.212428	+	1.98869i	2.10366	+	0.563673i	−0.226151	+	0.147137i	2.90151	−	1.67519i	1.65669	−	2.29246i	2.56656	+	1.48180i	−1.67966	−	2.58165i
269.18	−0.997433	+	1.00256i	−0.152061	+	0.567500i	−0.0102532	−	1.99997i	2.89677	+	0.776187i	−0.417282	−	0.718493i	−0.532186	+	0.307258i	2.01532	+	1.98456i	2.29914	+	1.32741i	−3.66751	+	2.12999i
269.19	−0.991099	+	1.00882i	−0.545499	+	2.03583i	−0.0354459	−	1.99969i	0.540836	+	0.144916i	−1.51315	−	2.56802i	−3.82753	+	2.20983i	2.05246	+	1.94613i	−1.24895	−	0.721082i	−0.682217	+	0.401981i
269.20	−0.923666	−	1.07091i	0.716552	−	2.67421i	−0.293682	+	1.97832i	−1.17874	−	0.315843i	−3.52568	+	1.70272i	2.73293	−	1.57786i	2.38986	−	1.51280i	−4.03987	−	2.33242i	0.750525	+	1.55405i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
16.e	even	4	1	inner
37.c	even	3	1	inner
592.bj	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	592.2.bj.a	✓	296
16.e	even	4	1	inner	592.2.bj.a	✓	296
37.c	even	3	1	inner	592.2.bj.a	✓	296
592.bj	even	12	1	inner	592.2.bj.a	✓	296

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
592.2.bj.a	✓	296	1.a	even	1	1	trivial
592.2.bj.a	✓	296	16.e	even	4	1	inner
592.2.bj.a	✓	296	37.c	even	3	1	inner
592.2.bj.a	✓	296	592.bj	even	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(592, [\chi])\).