Newform orbit 540.3.c.a

• Label: 540.3.c.a
• Level: $540$
• Weight: $3$
• Character orbit: 540.c
• Analytic conductor: $14.714$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	540.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.7139342755\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 2 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
271.1	−1.96820	−	0.355251i		0		3.74759	+	1.39841i	−2.23607				0				6.30957i	−6.87922	−	4.08367i		0		4.40102	+	0.794365i
271.2	−1.96820	+	0.355251i		0		3.74759	−	1.39841i	−2.23607				0			−	6.30957i	−6.87922	+	4.08367i		0		4.40102	−	0.794365i
271.3	−1.96522	−	0.371367i		0		3.72417	+	1.45964i	2.23607				0				4.96192i	−6.77676	−	4.25154i		0		−4.39436	−	0.830402i
271.4	−1.96522	+	0.371367i		0		3.72417	−	1.45964i	2.23607				0			−	4.96192i	−6.77676	+	4.25154i		0		−4.39436	+	0.830402i
271.5	−1.65065	−	1.12932i		0		1.44928	+	3.72822i	−2.23607				0			−	7.54770i	1.81810	−	7.79067i		0		3.69096	+	2.52523i
271.6	−1.65065	+	1.12932i		0		1.44928	−	3.72822i	−2.23607				0				7.54770i	1.81810	+	7.79067i		0		3.69096	−	2.52523i
271.7	−1.54565	−	1.26924i		0		0.778062	+	3.92360i	2.23607				0			−	7.01322i	3.77737	−	7.05205i		0		−3.45618	−	2.83811i
271.8	−1.54565	+	1.26924i		0		0.778062	−	3.92360i	2.23607				0				7.01322i	3.77737	+	7.05205i		0		−3.45618	+	2.83811i
271.9	−1.31032	−	1.51098i		0		−0.566141	+	3.95973i	−2.23607				0				13.3433i	6.72491	−	4.33307i		0		2.92996	+	3.37866i
271.10	−1.31032	+	1.51098i		0		−0.566141	−	3.95973i	−2.23607				0			−	13.3433i	6.72491	+	4.33307i		0		2.92996	−	3.37866i
271.11	−0.976600	−	1.74535i		0		−2.09251	+	3.40902i	2.23607				0			−	4.47108i	7.99348	+	0.322911i		0		−2.18374	−	3.90273i
271.12	−0.976600	+	1.74535i		0		−2.09251	−	3.40902i	2.23607				0				4.47108i	7.99348	−	0.322911i		0		−2.18374	+	3.90273i
271.13	−0.361099	−	1.96713i		0		−3.73921	+	1.42066i	−2.23607				0			−	7.43331i	4.14485	+	6.84253i		0		0.807443	+	4.39864i
271.14	−0.361099	+	1.96713i		0		−3.73921	−	1.42066i	−2.23607				0				7.43331i	4.14485	−	6.84253i		0		0.807443	−	4.39864i
271.15	−0.315242	−	1.97500i		0		−3.80125	+	1.24520i	−2.23607				0			−	0.355913i	3.65759	+	7.11492i		0		0.704902	+	4.41623i
271.16	−0.315242	+	1.97500i		0		−3.80125	−	1.24520i	−2.23607				0				0.355913i	3.65759	−	7.11492i		0		0.704902	−	4.41623i
271.17	0.315242	−	1.97500i		0		−3.80125	−	1.24520i	2.23607				0				0.355913i	−3.65759	+	7.11492i		0		0.704902	−	4.41623i
271.18	0.315242	+	1.97500i		0		−3.80125	+	1.24520i	2.23607				0			−	0.355913i	−3.65759	−	7.11492i		0		0.704902	+	4.41623i
271.19	0.361099	−	1.96713i		0		−3.73921	−	1.42066i	2.23607				0				7.43331i	−4.14485	+	6.84253i		0		0.807443	−	4.39864i
271.20	0.361099	+	1.96713i		0		−3.73921	+	1.42066i	2.23607				0			−	7.43331i	−4.14485	−	6.84253i		0		0.807443	+	4.39864i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
4.b	odd	2	1	inner
12.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	540.3.c.a	✓	32
3.b	odd	2	1	inner	540.3.c.a	✓	32
4.b	odd	2	1	inner	540.3.c.a	✓	32
12.b	even	2	1	inner	540.3.c.a	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
540.3.c.a	✓	32	1.a	even	1	1	trivial
540.3.c.a	✓	32	3.b	odd	2	1	inner
540.3.c.a	✓	32	4.b	odd	2	1	inner
540.3.c.a	✓	32	12.b	even	2	1	inner