Newform orbit 760.2.cg.a

• Label: 760.2.cg.a
• Level: $760$
• Weight: $2$
• Character orbit: 760.cg
• Analytic conductor: $6.069$
• Analytic rank: $0$
• Dimension: $180$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.cg (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.06863055362\)
Analytic rank:	\(0\)
Dimension:	\(180\)
Relative dimension:	\(30\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 180 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
9.1		0		−2.02905	−	2.41812i		0		0.999810	−	2.00009i		0		−3.90153	−	2.25255i		0		−1.20935	+	6.85855i		0
9.2		0		−1.95654	−	2.33171i		0		−2.01241	−	0.974783i		0		2.59943	+	1.50078i		0		−1.08790	+	6.16977i		0
9.3		0		−1.94051	−	2.31261i		0		−1.89985	+	1.17922i		0		−1.86192	−	1.07498i		0		−1.06164	+	6.02088i		0
9.4		0		−1.78271	−	2.12455i		0		0.732601	+	2.11265i		0		−0.0747726	−	0.0431700i		0		−0.814719	+	4.62050i		0
9.5		0		−1.68162	−	2.00408i		0		0.278584	−	2.21865i		0		2.80508	+	1.61951i		0		−0.667539	+	3.78580i		0
9.6		0		−1.54150	−	1.83709i		0		2.07828	+	0.825083i		0		−1.10852	−	0.640004i		0		−0.477724	+	2.70931i		0
9.7		0		−1.09840	−	1.30903i		0		0.796248	+	2.08949i		0		4.20442	+	2.42742i		0		0.0138851	−	0.0787461i		0
9.8		0		−1.01318	−	1.20747i		0		−2.22120	−	0.257472i		0		1.36165	+	0.786149i		0		0.0895129	−	0.507653i		0
9.9		0		−0.877966	−	1.04632i		0		2.18448	−	0.477562i		0		0.903126	+	0.521420i		0		0.196985	−	1.11716i		0
9.10		0		−0.803370	−	0.957419i		0		0.829911	+	2.07635i		0		−3.19043	−	1.84200i		0		0.249696	−	1.41610i		0
9.11		0		−0.697018	−	0.830674i		0		−0.427258	−	2.19487i		0		−3.78151	−	2.18326i		0		0.316760	−	1.79643i		0
9.12		0		−0.688030	−	0.819963i		0		−1.70801	−	1.44315i		0		−0.376902	−	0.217604i		0		0.321992	−	1.82611i		0
9.13		0		−0.248287	−	0.295897i		0		2.19862	−	0.407498i		0		−1.75773	−	1.01483i		0		0.495036	−	2.80749i		0
9.14		0		−0.151401	−	0.180433i		0		0.549807	−	2.16742i		0		1.65647	+	0.956361i		0		0.511311	−	2.89979i		0
9.15		0		−0.0685383	−	0.0816808i		0		−0.163476	−	2.23008i		0		2.84561	+	1.64291i		0		0.518970	−	2.94323i		0
9.16		0		0.0685383	+	0.0816808i		0		−1.55870	+	1.60326i		0		−2.84561	−	1.64291i		0		0.518970	−	2.94323i		0
9.17		0		0.151401	+	0.180433i		0		−0.972015	+	2.01375i		0		−1.65647	−	0.956361i		0		0.511311	−	2.89979i		0
9.18		0		0.248287	+	0.295897i		0		1.42231	+	1.72541i		0		1.75773	+	1.01483i		0		0.495036	−	2.80749i		0
9.19		0		0.688030	+	0.819963i		0		−2.23605	+	0.00763171i		0		0.376902	+	0.217604i		0		0.321992	−	1.82611i		0
9.20		0		0.697018	+	0.830674i		0		−1.73813	+	1.40673i		0		3.78151	+	2.18326i		0		0.316760	−	1.79643i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
19.e	even	9	1	inner
95.p	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	760.2.cg.a	✓	180
5.b	even	2	1	inner	760.2.cg.a	✓	180
19.e	even	9	1	inner	760.2.cg.a	✓	180
95.p	even	18	1	inner	760.2.cg.a	✓	180

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
760.2.cg.a	✓	180	1.a	even	1	1	trivial
760.2.cg.a	✓	180	5.b	even	2	1	inner
760.2.cg.a	✓	180	19.e	even	9	1	inner
760.2.cg.a	✓	180	95.p	even	18	1	inner

Hecke kernels

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