Newform orbit 585.2.be.a

• Label: 585.2.be.a
• Level: $585$
• Weight: $2$
• Character orbit: 585.be
• Analytic conductor: $4.671$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.be (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.67124851824\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(80\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 160 q - 80 q^{4} - 16 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
259.1	−1.36676	+	2.36730i	−1.05005	−	1.37746i	−2.73607	−	4.73902i	2.15620	−	0.592286i	4.69603	−	0.603119i	−1.73160	+	2.99922i	9.49120			−0.794798	+	2.89280i	−1.54489	+	5.91389i
259.2	−1.36676	+	2.36730i	1.05005	+	1.37746i	−2.73607	−	4.73902i	−1.59103	+	1.57118i	−4.69603	+	0.603119i	−1.73160	+	2.99922i	9.49120			−0.794798	+	2.89280i	−1.54489	−	5.91389i
259.3	−1.32927	+	2.30236i	−1.07971	+	1.35433i	−2.53392	−	4.38888i	−0.615078	−	2.14981i	−1.68294	−	4.28617i	−0.724825	+	1.25543i	8.15598			−0.668438	−	2.92458i	5.76725	+	1.44154i
259.4	−1.32927	+	2.30236i	1.07971	−	1.35433i	−2.53392	−	4.38888i	−1.55425	−	1.60758i	1.68294	+	4.28617i	−0.724825	+	1.25543i	8.15598			−0.668438	−	2.92458i	5.76725	−	1.44154i
259.5	−1.29597	+	2.24468i	−1.61722	+	0.620164i	−2.35907	−	4.08603i	1.45482	+	1.69809i	0.703793	−	4.43386i	1.47985	−	2.56318i	7.04526			2.23079	−	2.00588i	−5.69707	+	1.06493i
259.6	−1.29597	+	2.24468i	1.61722	−	0.620164i	−2.35907	−	4.08603i	0.743181	+	2.10895i	−0.703793	+	4.43386i	1.47985	−	2.56318i	7.04526			2.23079	−	2.00588i	−5.69707	−	1.06493i
259.7	−1.17678	+	2.03824i	−0.101157	−	1.72909i	−1.76962	−	3.06507i	−2.13975	+	0.649205i	3.64335	+	1.82858i	0.684615	−	1.18579i	3.62269			−2.97953	+	0.349820i	1.19478	−	5.12530i
259.8	−1.17678	+	2.03824i	0.101157	+	1.72909i	−1.76962	−	3.06507i	1.63210	−	1.52848i	−3.64335	−	1.82858i	0.684615	−	1.18579i	3.62269			−2.97953	+	0.349820i	1.19478	+	5.12530i
259.9	−1.13478	+	1.96549i	−1.27035	−	1.17738i	−1.57544	−	2.72874i	0.152049	−	2.23089i	3.75569	−	1.16079i	2.42046	−	4.19236i	2.61198			0.227563	+	2.99136i	4.21226	+	2.83042i
259.10	−1.13478	+	1.96549i	1.27035	+	1.17738i	−1.57544	−	2.72874i	−2.00803	−	0.983768i	−3.75569	+	1.16079i	2.42046	−	4.19236i	2.61198			0.227563	+	2.99136i	4.21226	−	2.83042i
259.11	−1.10577	+	1.91525i	−0.848899	+	1.50976i	−1.44547	−	2.50362i	−1.43919	+	1.71135i	−1.95288	−	3.29531i	0.244460	−	0.423417i	1.97034			−1.55874	−	2.56327i	−1.68626	−	4.64878i
259.12	−1.10577	+	1.91525i	0.848899	−	1.50976i	−1.44547	−	2.50362i	2.20167	−	0.390697i	1.95288	+	3.29531i	0.244460	−	0.423417i	1.97034			−1.55874	−	2.56327i	−1.68626	+	4.64878i
259.13	−1.07221	+	1.85713i	−1.72069	−	0.198083i	−1.29928	−	2.25042i	−2.23533	+	0.0573849i	2.21281	−	2.98315i	−1.58700	+	2.74876i	1.28357			2.92153	+	0.681677i	2.29018	−	4.21282i
259.14	−1.07221	+	1.85713i	1.72069	+	0.198083i	−1.29928	−	2.25042i	1.16736	−	1.90716i	−2.21281	+	2.98315i	−1.58700	+	2.74876i	1.28357			2.92153	+	0.681677i	2.29018	+	4.21282i
259.15	−1.03184	+	1.78719i	−1.51087	−	0.846926i	−1.12937	−	1.95612i	0.242155	+	2.22292i	3.07258	−	1.82632i	−0.952559	+	1.64988i	0.533949			1.56543	+	2.55918i	−4.22264	−	1.86091i
259.16	−1.03184	+	1.78719i	1.51087	+	0.846926i	−1.12937	−	1.95612i	1.80403	+	1.32117i	−3.07258	+	1.82632i	−0.952559	+	1.64988i	0.533949			1.56543	+	2.55918i	−4.22264	+	1.86091i
259.17	−0.811422	+	1.40542i	−0.370710	+	1.69191i	−0.316810	−	0.548731i	1.65179	+	1.50718i	−2.07705	−	1.89386i	−1.78979	+	3.10000i	−2.21742			−2.72515	−	1.25442i	−3.45853	+	1.09850i
259.18	−0.811422	+	1.40542i	0.370710	−	1.69191i	−0.316810	−	0.548731i	0.479364	+	2.18408i	2.07705	+	1.89386i	−1.78979	+	3.10000i	−2.21742			−2.72515	−	1.25442i	−3.45853	−	1.09850i
259.19	−0.791768	+	1.37138i	−1.71581	+	0.236631i	−0.253794	−	0.439584i	2.23470	−	0.0782993i	1.03401	−	2.54039i	0.620317	−	1.07442i	−2.36329			2.88801	−	0.812027i	−1.66198	+	3.12662i
259.20	−0.791768	+	1.37138i	1.71581	−	0.236631i	−0.253794	−	0.439584i	−1.18516	+	1.89615i	−1.03401	+	2.54039i	0.620317	−	1.07442i	−2.36329			2.88801	−	0.812027i	−1.66198	−	3.12662i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
9.c	even	3	1	inner
13.b	even	2	1	inner
45.j	even	6	1	inner
65.d	even	2	1	inner
117.t	even	6	1	inner
585.be	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	585.2.be.a	✓	160
5.b	even	2	1	inner	585.2.be.a	✓	160
9.c	even	3	1	inner	585.2.be.a	✓	160
13.b	even	2	1	inner	585.2.be.a	✓	160
45.j	even	6	1	inner	585.2.be.a	✓	160
65.d	even	2	1	inner	585.2.be.a	✓	160
117.t	even	6	1	inner	585.2.be.a	✓	160
585.be	even	6	1	inner	585.2.be.a	✓	160

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
585.2.be.a	✓	160	1.a	even	1	1	trivial
585.2.be.a	✓	160	5.b	even	2	1	inner
585.2.be.a	✓	160	9.c	even	3	1	inner
585.2.be.a	✓	160	13.b	even	2	1	inner
585.2.be.a	✓	160	45.j	even	6	1	inner
585.2.be.a	✓	160	65.d	even	2	1	inner
585.2.be.a	✓	160	117.t	even	6	1	inner
585.2.be.a	✓	160	585.be	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(585, [\chi])\).