Newform orbit 960.2.cr.a

• Label: 960.2.cr.a
• Level: $960$
• Weight: $2$
• Character orbit: 960.cr
• Analytic conductor: $7.666$
• Analytic rank: $0$
• Dimension: $1504$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.cr (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.66563859404\)
Analytic rank:	\(0\)
Dimension:	\(1504\)
Relative dimension:	\(188\) over \(\Q(\zeta_{16})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1504 q - 8 q^{3} - 16 q^{6} - 16 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
53.1	−1.41421		8.25383e-5i	0.786362	+	1.54325i	2.00000		0.000233454i	0.596723	−	2.15498i	−1.11196	−	2.18256i	−1.59325	+	0.659947i	−2.82843		0.000495230i	−1.76327	+	2.42711i	−0.844072	+	3.04755i
53.2	−1.41387	+	0.0311571i	1.70558	−	0.301669i	1.99806	−	0.0881043i	−2.06137	−	0.866450i	−2.40207	+	0.479662i	0.678158	−	0.280902i	−2.82225	+	0.186822i	2.81799	−	1.02904i	2.94151	+	1.16082i
53.3	−1.41373	−	0.0368747i	0.245595	+	1.71455i	1.99728	+	0.104262i	2.17864	+	0.503523i	−0.283982	−	2.43297i	4.37418	−	1.81184i	−2.81978	−	0.221048i	−2.87937	+	0.842169i	−3.06145	−	0.792183i
53.4	−1.41371	+	0.0375838i	−0.801921	+	1.53523i	1.99717	−	0.106265i	−0.858226	+	2.06481i	1.07599	−	2.20051i	−1.10469	+	0.457579i	−2.81944	+	0.225290i	−1.71385	−	2.46226i	1.13568	−	2.95131i
53.5	−1.40918	−	0.119220i	0.160867	−	1.72456i	1.97157	+	0.336005i	−1.88565	+	1.20181i	−0.432294	+	2.41104i	0.489999	−	0.202964i	−2.73824	−	0.708543i	−2.94824	−	0.554852i	2.80049	−	1.46875i
53.6	−1.40905	−	0.120693i	−1.53416	−	0.803966i	1.97087	+	0.340126i	−1.35409	+	1.77945i	2.06468	+	1.31799i	1.93755	−	0.802560i	−2.73601	−	0.717126i	1.70728	+	2.46682i	2.12276	−	2.34391i
53.7	−1.40822	−	0.130016i	1.51751	−	0.834964i	1.96619	+	0.366182i	1.84126	+	1.26876i	−2.24555	+	0.978517i	−3.51273	+	1.45502i	−2.72123	−	0.771303i	1.60567	−	2.53413i	−2.42795	−	2.02610i
53.8	−1.39856	−	0.209819i	−0.750883	+	1.56083i	1.91195	+	0.586889i	2.17297	−	0.527461i	1.37765	−	2.02536i	−2.62460	+	1.08715i	−2.55084	−	1.22196i	−1.87235	−	2.34399i	−3.14970	+	0.281758i
53.9	−1.39429	−	0.236568i	0.685173	−	1.59077i	1.88807	+	0.659687i	1.10096	−	1.94625i	−1.33165	+	2.05589i	−1.12538	+	0.466149i	−2.47645	−	1.36645i	−2.06108	−	2.17990i	−1.99547	+	2.45318i
53.10	−1.39153	+	0.252257i	−1.64822	+	0.532311i	1.87273	−	0.702049i	−2.07983	−	0.821174i	2.15928	−	1.15651i	1.15122	−	0.476850i	−2.42887	+	1.44934i	2.43329	−	1.75474i	3.10129	+	0.618040i
53.11	−1.39132	−	0.253434i	1.47890	+	0.901590i	1.87154	+	0.705215i	−2.18405	+	0.479512i	−1.82913	−	1.62920i	−4.26107	+	1.76499i	−2.42519	−	1.45549i	1.37427	+	2.66672i	3.16023	−	0.113643i
53.12	−1.38987	+	0.261284i	1.73182	−	0.0280481i	1.86346	−	0.726299i	0.298174	−	2.21610i	−2.39968	+	0.491480i	3.03288	−	1.25626i	−2.40019	+	1.49635i	2.99843	−	0.0971488i	0.164608	+	3.15799i
53.13	−1.38612	−	0.280508i	−0.761534	−	1.55566i	1.84263	+	0.777633i	1.52531	+	1.63506i	0.619200	+	2.36993i	−3.36801	+	1.39508i	−2.33597	−	1.59476i	−1.84013	+	2.36937i	−1.65561	−	2.69425i
53.14	−1.37733	+	0.320881i	−1.68077	+	0.418326i	1.79407	−	0.883919i	2.23598	+	0.0198136i	2.18075	−	1.11550i	−1.77979	+	0.737211i	−2.18739	+	1.79313i	2.65001	−	1.40622i	−3.08604	+	0.690195i
53.15	−1.37448	+	0.332887i	1.19877	+	1.25018i	1.77837	−	0.915090i	0.764688	+	2.10125i	−2.06385	−	1.31928i	−1.40918	+	0.583701i	−2.13971	+	1.84977i	−0.125885	+	2.99736i	−1.75052	−	2.63357i
53.16	−1.37106	+	0.346691i	0.549751	−	1.64249i	1.75961	−	0.950669i	−1.53370	−	1.62719i	−0.184305	+	2.44255i	−3.25121	+	1.34669i	−2.08294	+	1.91347i	−2.39555	−	1.80592i	2.66693	+	1.69926i
53.17	−1.35113	−	0.417655i	−1.44379	−	0.956795i	1.65113	+	1.12862i	−0.865243	−	2.06188i	1.55115	+	1.89577i	−2.39826	+	0.993390i	−1.75952	−	2.21451i	1.16909	+	2.76283i	0.307905	+	3.14725i
53.18	−1.34734	−	0.429726i	−1.58974	−	0.687544i	1.63067	+	1.15798i	2.23195	+	0.135654i	1.84647	+	1.60951i	2.79559	−	1.15797i	−1.69946	−	2.26094i	2.05457	+	2.18604i	−2.94891	−	1.14190i
53.19	−1.34698	−	0.430854i	1.64044	−	0.555824i	1.62873	+	1.16071i	0.0417654	+	2.23568i	−2.44913	+	0.0418934i	3.06250	−	1.26853i	−1.69378	−	2.26520i	2.38212	−	1.82360i	0.906994	−	3.02942i
53.20	−1.33879	+	0.455681i	1.11340	−	1.32678i	1.58471	−	1.22012i	2.23561	+	0.0453608i	−0.886014	+	2.28363i	2.45663	−	1.01757i	−1.56560	+	2.35561i	−0.520693	−	2.95447i	−3.01368	+	0.957996i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
320.bc	odd	16	1	inner
960.cr	even	16	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	960.2.cr.a	yes	1504
3.b	odd	2	1	inner	960.2.cr.a	yes	1504
5.c	odd	4	1		960.2.cf.a	✓	1504
15.e	even	4	1		960.2.cf.a	✓	1504
64.i	even	16	1		960.2.cf.a	✓	1504
192.q	odd	16	1		960.2.cf.a	✓	1504
320.bc	odd	16	1	inner	960.2.cr.a	yes	1504
960.cr	even	16	1	inner	960.2.cr.a	yes	1504

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
960.2.cf.a	✓	1504	5.c	odd	4	1
960.2.cf.a	✓	1504	15.e	even	4	1
960.2.cf.a	✓	1504	64.i	even	16	1
960.2.cf.a	✓	1504	192.q	odd	16	1
960.2.cr.a	yes	1504	1.a	even	1	1	trivial
960.2.cr.a	yes	1504	3.b	odd	2	1	inner
960.2.cr.a	yes	1504	320.bc	odd	16	1	inner
960.2.cr.a	yes	1504	960.cr	even	16	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(960, [\chi])\).