Newform orbit 966.2.bf.a

• Label: 966.2.bf.a
• Level: $966$
• Weight: $2$
• Character orbit: 966.bf
• Analytic conductor: $7.714$
• Analytic rank: $0$
• Dimension: $1280$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.bf (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.71354883526\)
Analytic rank:	\(0\)
Dimension:	\(1280\)
Relative dimension:	\(64\) over \(\Q(\zeta_{66})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1280q - 64q^{4} - 8q^{6} + 4q^{9} + O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−0.458227	+	0.888835i	−1.72757	+	0.124485i	−0.580057	−	0.814576i	1.87856	+	1.79120i	0.680972	−	1.59257i	0.248917	+	2.63402i	0.989821	−	0.142315i	2.96901	−	0.430114i	−2.45289	+	0.848953i
11.2	−0.458227	+	0.888835i	−1.71624	+	0.233522i	−0.580057	−	0.814576i	−2.07174	−	1.97540i	0.578862	−	1.63246i	−2.59178	+	0.531663i	0.989821	−	0.142315i	2.89093	−	0.801559i	2.70513	−	0.936254i
11.3	−0.458227	+	0.888835i	−1.61819	+	0.617630i	−0.580057	−	0.814576i	2.31266	+	2.20512i	0.192526	−	1.72132i	−1.37219	−	2.26210i	0.989821	−	0.142315i	2.23707	−	1.99888i	−3.01971	+	1.04513i
11.4	−0.458227	+	0.888835i	−1.61477	−	0.626501i	−0.580057	−	0.814576i	−1.38105	−	1.31683i	1.29679	−	1.14819i	2.39472	+	1.12486i	0.989821	−	0.142315i	2.21499	+	2.02332i	1.80327	−	0.624119i
11.5	−0.458227	+	0.888835i	−1.59740	−	0.669558i	−0.580057	−	0.814576i	−1.48546	−	1.41639i	1.32710	−	1.11302i	0.598705	−	2.57712i	0.989821	−	0.142315i	2.10338	+	2.13911i	1.93961	−	0.671307i
11.6	−0.458227	+	0.888835i	−1.47486	+	0.908181i	−0.580057	−	0.814576i	0.367129	+	0.350057i	−0.131404	−	1.72706i	2.61845	−	0.379131i	0.989821	−	0.142315i	1.35042	−	2.67888i	−0.479371	+	0.165912i
11.7	−0.458227	+	0.888835i	−1.24755	−	1.20151i	−0.580057	−	0.814576i	2.79695	+	2.66688i	1.63960	−	0.558302i	2.62506	−	0.330282i	0.989821	−	0.142315i	0.112753	+	2.99788i	−3.65206	+	1.26399i
11.8	−0.458227	+	0.888835i	−1.17110	−	1.27614i	−0.580057	−	0.814576i	0.549032	+	0.523501i	1.67091	−	0.456154i	−2.28022	−	1.34186i	0.989821	−	0.142315i	−0.257056	+	2.98897i	−0.716888	+	0.248117i
11.9	−0.458227	+	0.888835i	−1.08373	−	1.35113i	−0.580057	−	0.814576i	0.598114	+	0.570300i	1.69752	−	0.344132i	−0.225504	+	2.63612i	0.989821	−	0.142315i	−0.651080	+	2.92850i	−0.780975	+	0.270298i
11.10	−0.458227	+	0.888835i	−1.07755	+	1.35606i	−0.580057	−	0.814576i	−1.05877	−	1.00954i	−0.711553	−	1.57914i	−2.64409	+	0.0936177i	0.989821	−	0.142315i	−0.677791	−	2.92243i	1.38247	−	0.478477i
11.11	−0.458227	+	0.888835i	−0.777131	+	1.54792i	−0.580057	−	0.814576i	−2.85699	−	2.72413i	−1.01975	−	1.40004i	2.56739	+	0.639162i	0.989821	−	0.142315i	−1.79214	−	2.40588i	3.73045	−	1.29112i
11.12	−0.458227	+	0.888835i	−0.484961	+	1.66277i	−0.580057	−	0.814576i	0.377293	+	0.359748i	−1.25571	−	1.19298i	−1.57508	−	2.12582i	0.989821	−	0.142315i	−2.52963	−	1.61276i	−0.492643	+	0.170505i
11.13	−0.458227	+	0.888835i	−0.418014	−	1.68085i	−0.580057	−	0.814576i	−2.21751	−	2.11439i	1.68555	+	0.398666i	0.589589	+	2.57922i	0.989821	−	0.142315i	−2.65053	+	1.40524i	2.89546	−	1.00213i
11.14	−0.458227	+	0.888835i	−0.349901	+	1.69634i	−0.580057	−	0.814576i	1.57677	+	1.50345i	−1.34743	−	1.08831i	1.82632	−	1.91430i	0.989821	−	0.142315i	−2.75514	−	1.18710i	−2.05883	+	0.712569i
11.15	−0.458227	+	0.888835i	−0.119815	−	1.72790i	−0.580057	−	0.814576i	0.424017	+	0.404299i	1.59072	+	0.685274i	−2.01888	+	1.71001i	0.989821	−	0.142315i	−2.97129	+	0.414058i	−0.553651	+	0.191621i
11.16	−0.458227	+	0.888835i	−0.118210	−	1.72801i	−0.580057	−	0.814576i	0.829499	+	0.790926i	1.59009	+	0.686752i	2.21783	−	1.44264i	0.989821	−	0.142315i	−2.97205	+	0.408537i	−1.08310	+	0.374865i
11.17	−0.458227	+	0.888835i	0.111990	+	1.72843i	−0.580057	−	0.814576i	−0.770390	−	0.734565i	−1.58760	−	0.692470i	0.520510	+	2.59405i	0.989821	−	0.142315i	−2.97492	+	0.387134i	1.00592	−	0.348153i
11.18	−0.458227	+	0.888835i	0.328863	−	1.70054i	−0.580057	−	0.814576i	−2.51640	−	2.39938i	1.36081	+	1.07154i	2.33268	−	1.24844i	0.989821	−	0.142315i	−2.78370	−	1.11849i	3.28573	−	1.13720i
11.19	−0.458227	+	0.888835i	0.375913	−	1.69077i	−0.580057	−	0.814576i	3.10185	+	2.95761i	1.33056	+	1.10888i	−1.66460	−	2.05648i	0.989821	−	0.142315i	−2.71738	−	1.27116i	−4.05017	+	1.40178i
11.20	−0.458227	+	0.888835i	0.470566	+	1.66690i	−0.580057	−	0.814576i	2.48669	+	2.37105i	−1.69723	−	0.345564i	1.41557	+	2.23521i	0.989821	−	0.142315i	−2.55714	+	1.56878i	−3.24694	+	1.12378i

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.d	odd	22	1	inner
69.g	even	22	1	inner
161.p	odd	66	1	inner
483.bc	even	66	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	966.2.bf.a	✓	1280
3.b	odd	2	1	inner	966.2.bf.a	✓	1280
7.c	even	3	1	inner	966.2.bf.a	✓	1280
21.h	odd	6	1	inner	966.2.bf.a	✓	1280
23.d	odd	22	1	inner	966.2.bf.a	✓	1280
69.g	even	22	1	inner	966.2.bf.a	✓	1280
161.p	odd	66	1	inner	966.2.bf.a	✓	1280
483.bc	even	66	1	inner	966.2.bf.a	✓	1280

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
966.2.bf.a	✓	1280	1.a	even	1	1	trivial
966.2.bf.a	✓	1280	3.b	odd	2	1	inner
966.2.bf.a	✓	1280	7.c	even	3	1	inner
966.2.bf.a	✓	1280	21.h	odd	6	1	inner
966.2.bf.a	✓	1280	23.d	odd	22	1	inner
966.2.bf.a	✓	1280	69.g	even	22	1	inner
966.2.bf.a	✓	1280	161.p	odd	66	1	inner
966.2.bf.a	✓	1280	483.bc	even	66	1	inner

Hecke kernels

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