Newform orbit 1140.2.u.a

• Label: 1140.2.u.a
• Level: $1140$
• Weight: $2$
• Character orbit: 1140.u
• Analytic conductor: $9.103$
• Analytic rank: $0$
• Dimension: $36$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1140.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.10294583043\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Relative dimension:	\(18\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 36 q - 2 q^{3} - 4 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
77.1		0		−1.72892	+	0.104120i		0		−1.25027	−	1.85387i		0		1.53683	+	1.53683i		0		2.97832	−	0.360031i		0
77.2		0		−1.67131	−	0.454653i		0		1.74808	+	1.39436i		0		2.11114	+	2.11114i		0		2.58658	+	1.51974i		0
77.3		0		−1.51962	+	0.831114i		0		−0.584734	+	2.15826i		0		−0.319747	−	0.319747i		0		1.61850	−	2.52596i		0
77.4		0		−1.49248	+	0.878917i		0		2.22480	+	0.224229i		0		−1.69928	−	1.69928i		0		1.45501	−	2.62354i		0
77.5		0		−1.17415	−	1.27333i		0		0.349474	−	2.20859i		0		−2.74157	−	2.74157i		0		−0.242724	+	2.99016i		0
77.6		0		−0.878917	+	1.49248i		0		−2.22480	−	0.224229i		0		−1.69928	−	1.69928i		0		−1.45501	−	2.62354i		0
77.7		0		−0.865276	−	1.50043i		0		−1.09331	+	1.95056i		0		−0.902876	−	0.902876i		0		−1.50259	+	2.59658i		0
77.8		0		−0.831114	+	1.51962i		0		0.584734	−	2.15826i		0		−0.319747	−	0.319747i		0		−1.61850	−	2.52596i		0
77.9		0		−0.246513	−	1.71442i		0		1.60612	+	1.55575i		0		3.36156	+	3.36156i		0		−2.87846	+	0.845254i		0
77.10		0		−0.104120	+	1.72892i		0		1.25027	+	1.85387i		0		1.53683	+	1.53683i		0		−2.97832	−	0.360031i		0
77.11		0		0.454653	+	1.67131i		0		−1.74808	−	1.39436i		0		2.11114	+	2.11114i		0		−2.58658	+	1.51974i		0
77.12		0		0.652056	−	1.60463i		0		−2.13223	+	0.673490i		0		1.04147	+	1.04147i		0		−2.14965	−	2.09261i		0
77.13		0		0.753222	−	1.55970i		0		−1.28294	−	1.83141i		0		−3.38752	−	3.38752i		0		−1.86531	−	2.34960i		0
77.14		0		1.27333	+	1.17415i		0		−0.349474	+	2.20859i		0		−2.74157	−	2.74157i		0		0.242724	+	2.99016i		0
77.15		0		1.50043	+	0.865276i		0		1.09331	−	1.95056i		0		−0.902876	−	0.902876i		0		1.50259	+	2.59658i		0
77.16		0		1.55970	−	0.753222i		0		1.28294	+	1.83141i		0		−3.38752	−	3.38752i		0		1.86531	−	2.34960i		0
77.17		0		1.60463	−	0.652056i		0		2.13223	−	0.673490i		0		1.04147	+	1.04147i		0		2.14965	−	2.09261i		0
77.18		0		1.71442	+	0.246513i		0		−1.60612	−	1.55575i		0		3.36156	+	3.36156i		0		2.87846	+	0.845254i		0
533.1		0		−1.72892	−	0.104120i		0		−1.25027	+	1.85387i		0		1.53683	−	1.53683i		0		2.97832	+	0.360031i		0
533.2		0		−1.67131	+	0.454653i		0		1.74808	−	1.39436i		0		2.11114	−	2.11114i		0		2.58658	−	1.51974i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.c	odd	4	1	inner
15.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1140.2.u.a	✓	36
3.b	odd	2	1	inner	1140.2.u.a	✓	36
5.c	odd	4	1	inner	1140.2.u.a	✓	36
15.e	even	4	1	inner	1140.2.u.a	✓	36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1140.2.u.a	✓	36	1.a	even	1	1	trivial
1140.2.u.a	✓	36	3.b	odd	2	1	inner
1140.2.u.a	✓	36	5.c	odd	4	1	inner
1140.2.u.a	✓	36	15.e	even	4	1	inner