Newform orbit 760.2.co.a

• Label: 760.2.co.a
• Level: $760$
• Weight: $2$
• Character orbit: 760.co
• Analytic conductor: $6.069$
• Analytic rank: $0$
• Dimension: $360$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.co (of order \(36\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.06863055362\)
Analytic rank:	\(0\)
Dimension:	\(360\)
Relative dimension:	\(30\) over \(\Q(\zeta_{36})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 360 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
33.1		0		−1.87266	−	2.67443i		0		−0.657526	−	2.13721i		0		3.03482	+	0.813178i		0		−2.61968	+	7.19751i		0
33.2		0		−1.81268	−	2.58877i		0		2.05719	+	0.876331i		0		0.123641	+	0.0331295i		0		−2.38988	+	6.56614i		0
33.3		0		−1.70479	−	2.43469i		0		−0.955362	+	2.02170i		0		3.02003	+	0.809214i		0		−1.99535	+	5.48218i		0
33.4		0		−1.48525	−	2.12115i		0		−2.14758	−	0.622820i		0		−3.32456	−	0.890814i		0		−1.26727	+	3.48180i		0
33.5		0		−1.33571	−	1.90759i		0		−1.68315	+	1.47207i		0		0.610837	+	0.163673i		0		−0.828721	+	2.27689i		0
33.6		0		−1.17045	−	1.67158i		0		0.833703	+	2.07483i		0		−4.35255	−	1.16626i		0		−0.398156	+	1.09392i		0
33.7		0		−1.11856	−	1.59747i		0		1.83270	+	1.28110i		0		2.88302	+	0.772503i		0		−0.274674	+	0.754660i		0
33.8		0		−0.975756	−	1.39352i		0		−0.499440	−	2.17958i		0		−1.09418	−	0.293185i		0		0.0362511	−	0.0995992i		0
33.9		0		−0.961244	−	1.37280i		0		2.02099	−	0.956861i		0		−2.94465	−	0.789017i		0		0.0654750	−	0.179891i		0
33.10		0		−0.808307	−	1.15438i		0		1.08150	−	1.95713i		0		2.17014	+	0.581488i		0		0.346823	−	0.952887i		0
33.11		0		−0.772151	−	1.10275i		0		−1.66372	−	1.49400i		0		0.759256	+	0.203442i		0		0.406228	−	1.11610i		0
33.12		0		−0.588308	−	0.840191i		0		−0.0701490	+	2.23497i		0		−1.50551	−	0.403401i		0		0.666246	−	1.83050i		0
33.13		0		−0.399936	−	0.571168i		0		1.70949	+	1.44140i		0		2.74141	+	0.734558i		0		0.859777	−	2.36222i		0
33.14		0		−0.0151620	−	0.0216536i		0		−1.55699	+	1.60492i		0		−0.954785	−	0.255834i		0		1.02582	−	2.81842i		0
33.15		0		0.122567	+	0.175045i		0		2.23547	−	0.0518275i		0		−3.94272	−	1.05645i		0		1.01044	−	2.77617i		0
33.16		0		0.178929	+	0.255537i		0		−1.93540	−	1.11992i		0		−2.84819	−	0.763171i		0		0.992777	−	2.72763i		0
33.17		0		0.321418	+	0.459033i		0		2.20304	+	0.382896i		0		2.13377	+	0.571743i		0		0.918659	−	2.52399i		0
33.18		0		0.349915	+	0.499730i		0		−2.21686	+	0.292423i		0		4.50155	+	1.20619i		0		0.898771	−	2.46935i		0
33.19		0		0.421297	+	0.601675i		0		0.455539	−	2.18917i		0		−3.10049	−	0.830773i		0		0.841539	−	2.31211i		0
33.20		0		0.484029	+	0.691265i		0		−1.80196	−	1.32399i		0		1.60236	+	0.429351i		0		0.782497	−	2.14989i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
19.f	odd	18	1	inner
95.r	even	36	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	760.2.co.a	✓	360
5.c	odd	4	1	inner	760.2.co.a	✓	360
19.f	odd	18	1	inner	760.2.co.a	✓	360
95.r	even	36	1	inner	760.2.co.a	✓	360

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
760.2.co.a	✓	360	1.a	even	1	1	trivial
760.2.co.a	✓	360	5.c	odd	4	1	inner
760.2.co.a	✓	360	19.f	odd	18	1	inner
760.2.co.a	✓	360	95.r	even	36	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(760, [\chi])\).