Newform orbit 483.2.v.a

• Label: 483.2.v.a
• Level: $483$
• Weight: $2$
• Character orbit: 483.v
• Analytic conductor: $3.857$
• Analytic rank: $0$
• Dimension: $600$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.v (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.85677441763\)
Analytic rank:	\(0\)
Dimension:	\(600\)
Relative dimension:	\(60\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 600 q + 20 q^{4} - 18 q^{7} - 26 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
41.1	−0.783018	+	2.66671i	−1.29371	+	1.15165i	−4.81573	−	3.09488i	0.328519	−	2.28490i	−2.05813	−	4.35173i	−2.59187	+	0.531216i	7.82307	−	6.77873i	0.347391	−	2.97982i	5.83594	+	2.66518i
41.2	−0.783018	+	2.66671i	1.29371	−	1.15165i	−4.81573	−	3.09488i	−0.328519	+	2.28490i	2.05813	+	4.35173i	2.09878	−	1.61094i	7.82307	−	6.77873i	0.347391	−	2.97982i	−5.83594	−	2.66518i
41.3	−0.698454	+	2.37872i	−1.39478	−	1.02693i	−3.48795	−	2.24157i	−0.386473	+	2.68798i	3.41696	−	2.60053i	0.0322339	+	2.64555i	4.02101	−	3.48422i	0.890837	+	2.86468i	−6.12401	−	2.79674i
41.4	−0.698454	+	2.37872i	1.39478	+	1.02693i	−3.48795	−	2.24157i	0.386473	−	2.68798i	−3.41696	+	2.60053i	1.97827	+	1.75683i	4.02101	−	3.48422i	0.890837	+	2.86468i	6.12401	+	2.79674i
41.5	−0.688131	+	2.34356i	−1.70257	+	0.318198i	−3.33623	−	2.14407i	−0.310810	+	2.16173i	0.425877	−	4.20904i	1.22272	−	2.34626i	3.62868	−	3.14427i	2.79750	−	1.08351i	−4.85226	−	2.21595i
41.6	−0.688131	+	2.34356i	1.70257	−	0.318198i	−3.33623	−	2.14407i	0.310810	−	2.16173i	−0.425877	+	4.20904i	−2.57390	−	0.612403i	3.62868	−	3.14427i	2.79750	−	1.08351i	4.85226	+	2.21595i
41.7	−0.659075	+	2.24460i	−0.178359	+	1.72284i	−2.92135	−	1.87744i	−0.169901	+	1.18169i	−3.74955	−	1.53583i	2.26497	+	1.36744i	2.60355	−	2.25599i	−2.93638	−	0.614570i	−2.54044	−	1.16018i
41.8	−0.659075	+	2.24460i	0.178359	−	1.72284i	−2.92135	−	1.87744i	0.169901	−	1.18169i	3.74955	+	1.53583i	−0.449799	+	2.60724i	2.60355	−	2.25599i	−2.93638	−	0.614570i	2.54044	+	1.16018i
41.9	−0.601323	+	2.04792i	−0.160145	+	1.72463i	−2.14987	−	1.38164i	−0.358395	+	2.49269i	−3.43560	−	1.36502i	−2.54603	+	0.719520i	0.896135	−	0.776505i	−2.94871	−	0.552383i	−4.88932	−	2.23288i
41.10	−0.601323	+	2.04792i	0.160145	−	1.72463i	−2.14987	−	1.38164i	0.358395	−	2.49269i	3.43560	+	1.36502i	2.21107	−	1.45298i	0.896135	−	0.776505i	−2.94871	−	0.552383i	4.88932	+	2.23288i
41.11	−0.549147	+	1.87022i	−1.59123	+	0.684091i	−1.51367	−	0.972774i	0.245423	−	1.70696i	−0.405583	−	3.35163i	2.55196	−	0.698205i	−0.295653	+	0.256185i	2.06404	−	2.17710i	3.05762	+	1.39637i
41.12	−0.549147	+	1.87022i	1.59123	−	0.684091i	−1.51367	−	0.972774i	−0.245423	+	1.70696i	0.405583	+	3.35163i	−2.19885	+	1.47142i	−0.295653	+	0.256185i	2.06404	−	2.17710i	−3.05762	−	1.39637i
41.13	−0.493988	+	1.68237i	−0.151912	+	1.72538i	−0.903836	−	0.580860i	0.558871	−	3.88703i	−2.82768	−	1.10789i	−0.0105749	−	2.64573i	−1.22655	+	1.06281i	−2.95385	−	0.524209i	6.26335	+	2.86037i
41.14	−0.493988	+	1.68237i	0.151912	−	1.72538i	−0.903836	−	0.580860i	−0.558871	+	3.88703i	2.82768	+	1.10789i	−1.99258	−	1.74058i	−1.22655	+	1.06281i	−2.95385	−	0.524209i	−6.26335	−	2.86037i
41.15	−0.468338	+	1.59501i	−1.57515	−	0.720338i	−0.642222	−	0.412731i	0.0822804	−	0.572273i	1.88665	−	2.17503i	−1.81311	−	1.92682i	−1.55355	+	1.34616i	1.96223	+	2.26929i	0.874248	+	0.399256i
41.16	−0.468338	+	1.59501i	1.57515	+	0.720338i	−0.642222	−	0.412731i	−0.0822804	+	0.572273i	−1.88665	+	2.17503i	−0.268855	−	2.63206i	−1.55355	+	1.34616i	1.96223	+	2.26929i	−0.874248	−	0.399256i
41.17	−0.454217	+	1.54692i	−1.66392	−	0.481000i	−0.504143	−	0.323993i	0.562316	−	3.91099i	1.49985	−	2.35548i	−1.48783	+	2.18778i	−1.70670	+	1.47886i	2.53728	+	1.60069i	5.79458	+	2.64630i
41.18	−0.454217	+	1.54692i	1.66392	+	0.481000i	−0.504143	−	0.323993i	−0.562316	+	3.91099i	−1.49985	+	2.35548i	2.62773	+	0.308264i	−1.70670	+	1.47886i	2.53728	+	1.60069i	−5.79458	−	2.64630i
41.19	−0.340118	+	1.15833i	−1.07735	−	1.35621i	0.456447	+	0.293341i	−0.0646472	+	0.449631i	1.93738	−	0.786663i	2.56225	+	0.659450i	−2.31977	+	2.01009i	−0.678624	+	2.92224i	−0.498836	−	0.227811i
41.20	−0.340118	+	1.15833i	1.07735	+	1.35621i	0.456447	+	0.293341i	0.0646472	−	0.449631i	−1.93738	+	0.786663i	−1.17954	+	2.36827i	−2.31977	+	2.01009i	−0.678624	+	2.92224i	0.498836	+	0.227811i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.b	odd	2	1	inner
21.c	even	2	1	inner
23.c	even	11	1	inner
69.h	odd	22	1	inner
161.l	odd	22	1	inner
483.v	even	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	483.2.v.a	✓	600
3.b	odd	2	1	inner	483.2.v.a	✓	600
7.b	odd	2	1	inner	483.2.v.a	✓	600
21.c	even	2	1	inner	483.2.v.a	✓	600
23.c	even	11	1	inner	483.2.v.a	✓	600
69.h	odd	22	1	inner	483.2.v.a	✓	600
161.l	odd	22	1	inner	483.2.v.a	✓	600
483.v	even	22	1	inner	483.2.v.a	✓	600

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
483.2.v.a	✓	600	1.a	even	1	1	trivial
483.2.v.a	✓	600	3.b	odd	2	1	inner
483.2.v.a	✓	600	7.b	odd	2	1	inner
483.2.v.a	✓	600	21.c	even	2	1	inner
483.2.v.a	✓	600	23.c	even	11	1	inner
483.2.v.a	✓	600	69.h	odd	22	1	inner
483.2.v.a	✓	600	161.l	odd	22	1	inner
483.2.v.a	✓	600	483.v	even	22	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(483, [\chi])\).