Newform orbit 165.2.v.a

• Label: 165.2.v.a
• Level: $165$
• Weight: $2$
• Character orbit: 165.v
• Analytic conductor: $1.318$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.v (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.31753163335\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(20\) over \(\Q(\zeta_{20})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 160 q - 8 q^{3} - 12 q^{6} - 20 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
38.1	−1.20106	+	2.35721i	−1.70986	−	0.276357i	−2.93833	−	4.04427i	0.620713	−	2.14819i	2.70508	−	3.69858i	−0.349884	+	2.20908i	7.83634	−	1.24115i	2.84725	+	0.945066i	4.31822	+	4.04325i
38.2	−1.05798	+	2.07639i	1.42761	−	0.980774i	−2.01653	−	2.77551i	2.15856	−	0.583621i	0.526092	+	4.00192i	0.378371	−	2.38894i	3.29310	−	0.521576i	1.07616	−	2.80033i	−1.07188	+	5.09948i
38.3	−1.01480	+	1.99165i	0.203413	−	1.72006i	−1.76128	−	2.42420i	−1.92730	+	1.13380i	3.21934	+	2.15064i	−0.500702	+	3.16131i	2.19997	−	0.348441i	−2.91725	−	0.699767i	−0.302306	−	4.98909i
38.4	−0.958847	+	1.88184i	−0.765924	+	1.55350i	−1.44638	−	1.99077i	0.264574	+	2.22036i	−2.18904	−	2.93092i	−0.184103	+	1.16238i	0.961090	−	0.152222i	−1.82672	−	2.37972i	−4.43206	−	1.63110i
38.5	−0.700887	+	1.37557i	1.55912	+	0.754410i	−0.225374	−	0.310201i	−1.44615	−	1.70548i	−2.13051	+	1.61592i	−0.579429	+	3.65837i	−2.46499	+	0.390417i	1.86173	+	2.35244i	3.35959	−	0.793931i
38.6	−0.531621	+	1.04336i	1.72137	+	0.192059i	0.369582	+	0.508686i	−0.292350	+	2.21687i	−1.11550	+	1.69391i	0.356697	−	2.25209i	−3.04038	+	0.481549i	2.92623	+	0.661209i	−2.15759	−	1.48356i
38.7	−0.493426	+	0.968403i	−0.511262	−	1.65488i	0.481235	+	0.662363i	−0.996156	−	2.00192i	1.85486	+	0.321451i	0.654138	−	4.13007i	−3.02585	+	0.479248i	−2.47722	+	1.69215i	2.43019	+	0.0231181i
38.8	−0.440221	+	0.863982i	−1.72156	−	0.190380i	0.622900	+	0.857349i	2.21116	+	0.332794i	0.922350	−	1.40358i	0.0473285	−	0.298820i	−2.93041	+	0.464131i	2.92751	+	0.655500i	−1.26093	+	1.76390i
38.9	−0.218927	+	0.429668i	0.374540	+	1.69107i	1.03889	+	1.42990i	2.07671	−	0.829030i	−0.808595	−	0.209292i	0.194792	−	1.22987i	−1.79440	+	0.284205i	−2.71944	+	1.26675i	−0.0984387	+	1.07379i
38.10	−0.0299461	+	0.0587726i	0.903860	−	1.47751i	1.17301	+	1.61451i	1.28184	−	1.83218i	0.0597700	+	0.0973679i	−0.511898	+	3.23200i	−0.260316	+	0.0412300i	−1.36607	−	2.67093i	0.0692960	+	0.130204i
38.11	0.0299461	−	0.0587726i	−1.31620	−	1.12589i	1.17301	+	1.61451i	−1.28184	+	1.83218i	−0.105586	+	0.0436404i	−0.511898	+	3.23200i	0.260316	−	0.0412300i	0.464754	+	2.96378i	0.0692960	+	0.130204i
38.12	0.218927	−	0.429668i	0.166360	+	1.72404i	1.03889	+	1.42990i	−2.07671	+	0.829030i	0.777186	+	0.305959i	0.194792	−	1.22987i	1.79440	−	0.284205i	−2.94465	+	0.573625i	−0.0984387	+	1.07379i
38.13	0.440221	−	0.863982i	1.57847	−	0.713052i	0.622900	+	0.857349i	−2.21116	−	0.332794i	0.0788093	−	1.67767i	0.0473285	−	0.298820i	2.93041	−	0.464131i	1.98311	−	2.25106i	−1.26093	+	1.76390i
38.14	0.493426	−	0.968403i	−0.0251458	−	1.73187i	0.481235	+	0.662363i	0.996156	+	2.00192i	−1.68955	−	0.830198i	0.654138	−	4.13007i	3.02585	−	0.479248i	−2.99874	+	0.0870984i	2.43019	+	0.0231181i
38.15	0.531621	−	1.04336i	−1.57777	+	0.714592i	0.369582	+	0.508686i	0.292350	−	2.21687i	−0.0931960	+	2.02608i	0.356697	−	2.25209i	3.04038	−	0.481549i	1.97872	−	2.25492i	−2.15759	−	1.48356i
38.16	0.700887	−	1.37557i	−1.24969	+	1.19928i	−0.225374	−	0.310201i	1.44615	+	1.70548i	0.773803	+	2.55959i	−0.579429	+	3.65837i	2.46499	−	0.390417i	0.123446	−	2.99746i	3.35959	−	0.793931i
38.17	0.958847	−	1.88184i	1.20849	+	1.24078i	−1.44638	−	1.99077i	−0.264574	−	2.22036i	3.49372	−	1.08448i	−0.184103	+	1.16238i	−0.961090	+	0.152222i	−0.0790818	+	2.99896i	−4.43206	−	1.63110i
38.18	1.01480	−	1.99165i	−0.724986	−	1.57302i	−1.76128	−	2.42420i	1.92730	−	1.13380i	−3.86862	−	0.152376i	−0.500702	+	3.16131i	−2.19997	+	0.348441i	−1.94879	+	2.28084i	−0.302306	−	4.98909i
38.19	1.05798	−	2.07639i	−1.66082	−	0.491615i	−2.01653	−	2.77551i	−2.15856	+	0.583621i	−2.77789	+	2.92840i	0.378371	−	2.38894i	−3.29310	+	0.521576i	2.51663	+	1.63296i	−1.07188	+	5.09948i
38.20	1.20106	−	2.35721i	1.54078	−	0.791208i	−2.93833	−	4.04427i	−0.620713	+	2.14819i	−0.0144811	−	4.58222i	−0.349884	+	2.20908i	−7.83634	+	1.24115i	1.74798	−	2.43815i	4.31822	+	4.04325i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.c	odd	4	1	inner
11.c	even	5	1	inner
15.e	even	4	1	inner
33.h	odd	10	1	inner
55.k	odd	20	1	inner
165.v	even	20	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	165.2.v.a	✓	160
3.b	odd	2	1	inner	165.2.v.a	✓	160
5.b	even	2	1		825.2.ct.b		160
5.c	odd	4	1	inner	165.2.v.a	✓	160
5.c	odd	4	1		825.2.ct.b		160
11.c	even	5	1	inner	165.2.v.a	✓	160
15.d	odd	2	1		825.2.ct.b		160
15.e	even	4	1	inner	165.2.v.a	✓	160
15.e	even	4	1		825.2.ct.b		160
33.h	odd	10	1	inner	165.2.v.a	✓	160
55.j	even	10	1		825.2.ct.b		160
55.k	odd	20	1	inner	165.2.v.a	✓	160
55.k	odd	20	1		825.2.ct.b		160
165.o	odd	10	1		825.2.ct.b		160
165.v	even	20	1	inner	165.2.v.a	✓	160
165.v	even	20	1		825.2.ct.b		160

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
165.2.v.a	✓	160	1.a	even	1	1	trivial
165.2.v.a	✓	160	3.b	odd	2	1	inner
165.2.v.a	✓	160	5.c	odd	4	1	inner
165.2.v.a	✓	160	11.c	even	5	1	inner
165.2.v.a	✓	160	15.e	even	4	1	inner
165.2.v.a	✓	160	33.h	odd	10	1	inner
165.2.v.a	✓	160	55.k	odd	20	1	inner
165.2.v.a	✓	160	165.v	even	20	1	inner
825.2.ct.b		160	5.b	even	2	1
825.2.ct.b		160	5.c	odd	4	1
825.2.ct.b		160	15.d	odd	2	1
825.2.ct.b		160	15.e	even	4	1
825.2.ct.b		160	55.j	even	10	1
825.2.ct.b		160	55.k	odd	20	1
825.2.ct.b		160	165.o	odd	10	1
825.2.ct.b		160	165.v	even	20	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(165, [\chi])\).