Newform orbit 966.2.j.a

• Label: 966.2.j.a
• Level: $966$
• Weight: $2$
• Character orbit: 966.j
• Analytic conductor: $7.714$
• Analytic rank: $0$
• Dimension: $128$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.71354883526\)
Analytic rank:	\(0\)
Dimension:	\(128\)
Relative dimension:	\(64\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
137.1	−0.866025	+	0.500000i	−1.70593	+	0.299664i	0.500000	−	0.866025i	−0.915921	−	1.58642i	1.32755	−	1.11248i	1.74832	+	1.98579i			1.00000i	2.82040	−	1.02241i	1.58642	+	0.915921i
137.2	−0.866025	+	0.500000i	−1.70593	+	0.299664i	0.500000	−	0.866025i	0.915921	+	1.58642i	1.32755	−	1.11248i	−1.74832	−	1.98579i			1.00000i	2.82040	−	1.02241i	−1.58642	−	0.915921i
137.3	−0.866025	+	0.500000i	−1.62530	+	0.598665i	0.500000	−	0.866025i	−1.08784	−	1.88420i	1.10822	−	1.33111i	2.11385	−	1.59112i			1.00000i	2.28320	−	1.94602i	1.88420	+	1.08784i
137.4	−0.866025	+	0.500000i	−1.62530	+	0.598665i	0.500000	−	0.866025i	1.08784	+	1.88420i	1.10822	−	1.33111i	−2.11385	+	1.59112i			1.00000i	2.28320	−	1.94602i	−1.88420	−	1.08784i
137.5	−0.866025	+	0.500000i	−1.58146	−	0.706395i	0.500000	−	0.866025i	−1.53878	−	2.66525i	1.72278	−	0.178972i	−0.379647	−	2.61837i			1.00000i	2.00201	+	2.23427i	2.66525	+	1.53878i
137.6	−0.866025	+	0.500000i	−1.58146	−	0.706395i	0.500000	−	0.866025i	1.53878	+	2.66525i	1.72278	−	0.178972i	0.379647	+	2.61837i			1.00000i	2.00201	+	2.23427i	−2.66525	−	1.53878i
137.7	−0.866025	+	0.500000i	−1.34224	−	1.09471i	0.500000	−	0.866025i	−0.485598	−	0.841080i	1.70977	+	0.276923i	−0.839629	+	2.50899i			1.00000i	0.603233	+	2.93873i	0.841080	+	0.485598i
137.8	−0.866025	+	0.500000i	−1.34224	−	1.09471i	0.500000	−	0.866025i	0.485598	+	0.841080i	1.70977	+	0.276923i	0.839629	−	2.50899i			1.00000i	0.603233	+	2.93873i	−0.841080	−	0.485598i
137.9	−0.866025	+	0.500000i	−1.25907	+	1.18943i	0.500000	−	0.866025i	−1.82493	−	3.16086i	0.495676	−	1.65961i	−2.63810	−	0.201024i			1.00000i	0.170531	−	2.99515i	3.16086	+	1.82493i
137.10	−0.866025	+	0.500000i	−1.25907	+	1.18943i	0.500000	−	0.866025i	1.82493	+	3.16086i	0.495676	−	1.65961i	2.63810	+	0.201024i			1.00000i	0.170531	−	2.99515i	−3.16086	−	1.82493i
137.11	−0.866025	+	0.500000i	−0.608468	+	1.62166i	0.500000	−	0.866025i	−0.435291	−	0.753947i	−0.283879	−	1.70863i	−2.60300	−	0.473676i			1.00000i	−2.25953	−	1.97345i	0.753947	+	0.435291i
137.12	−0.866025	+	0.500000i	−0.608468	+	1.62166i	0.500000	−	0.866025i	0.435291	+	0.753947i	−0.283879	−	1.70863i	2.60300	+	0.473676i			1.00000i	−2.25953	−	1.97345i	−0.753947	−	0.435291i
137.13	−0.866025	+	0.500000i	−0.583589	−	1.63077i	0.500000	−	0.866025i	−1.70837	−	2.95898i	1.32079	+	1.12050i	2.46321	+	0.965707i			1.00000i	−2.31885	+	1.90340i	2.95898	+	1.70837i
137.14	−0.866025	+	0.500000i	−0.583589	−	1.63077i	0.500000	−	0.866025i	1.70837	+	2.95898i	1.32079	+	1.12050i	−2.46321	−	0.965707i			1.00000i	−2.31885	+	1.90340i	−2.95898	−	1.70837i
137.15	−0.866025	+	0.500000i	−0.498221	−	1.65885i	0.500000	−	0.866025i	−1.35083	−	2.33970i	1.26090	+	1.18749i	−2.62714	−	0.313267i			1.00000i	−2.50355	+	1.65295i	2.33970	+	1.35083i
137.16	−0.866025	+	0.500000i	−0.498221	−	1.65885i	0.500000	−	0.866025i	1.35083	+	2.33970i	1.26090	+	1.18749i	2.62714	+	0.313267i			1.00000i	−2.50355	+	1.65295i	−2.33970	−	1.35083i
137.17	−0.866025	+	0.500000i	0.144090	+	1.72605i	0.500000	−	0.866025i	−2.22533	−	3.85438i	−0.987809	−	1.42276i	1.67417	+	2.04869i			1.00000i	−2.95848	+	0.497412i	3.85438	+	2.22533i
137.18	−0.866025	+	0.500000i	0.144090	+	1.72605i	0.500000	−	0.866025i	2.22533	+	3.85438i	−0.987809	−	1.42276i	−1.67417	−	2.04869i			1.00000i	−2.95848	+	0.497412i	−3.85438	−	2.22533i
137.19	−0.866025	+	0.500000i	0.373762	+	1.69124i	0.500000	−	0.866025i	−0.437223	−	0.757293i	−1.16931	−	1.27778i	0.914719	−	2.48260i			1.00000i	−2.72060	+	1.26424i	0.757293	+	0.437223i
137.20	−0.866025	+	0.500000i	0.373762	+	1.69124i	0.500000	−	0.866025i	0.437223	+	0.757293i	−1.16931	−	1.27778i	−0.914719	+	2.48260i			1.00000i	−2.72060	+	1.26424i	−0.757293	−	0.437223i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.c	even	3	1	inner
21.h	odd	6	1	inner
23.b	odd	2	1	inner
69.c	even	2	1	inner
161.f	odd	6	1	inner
483.m	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	966.2.j.a	✓	128
3.b	odd	2	1	inner	966.2.j.a	✓	128
7.c	even	3	1	inner	966.2.j.a	✓	128
21.h	odd	6	1	inner	966.2.j.a	✓	128
23.b	odd	2	1	inner	966.2.j.a	✓	128
69.c	even	2	1	inner	966.2.j.a	✓	128
161.f	odd	6	1	inner	966.2.j.a	✓	128
483.m	even	6	1	inner	966.2.j.a	✓	128

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
966.2.j.a	✓	128	1.a	even	1	1	trivial
966.2.j.a	✓	128	3.b	odd	2	1	inner
966.2.j.a	✓	128	7.c	even	3	1	inner
966.2.j.a	✓	128	21.h	odd	6	1	inner
966.2.j.a	✓	128	23.b	odd	2	1	inner
966.2.j.a	✓	128	69.c	even	2	1	inner
966.2.j.a	✓	128	161.f	odd	6	1	inner
966.2.j.a	✓	128	483.m	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(966, [\chi])\).