Newform orbit 1116.2.p.a

• Label: 1116.2.p.a
• Level: $1116$
• Weight: $2$
• Character orbit: 1116.p
• Analytic conductor: $8.911$
• Analytic rank: $0$
• Dimension: $64$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1116 = 2^{2} \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1116.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.91130486557\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 64 q + 2 q^{7} + 2 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
533.1		0		−1.72772	+	0.122405i		0			−	0.991093i		0		3.47402				0		2.97003	−	0.422963i		0
533.2		0		−1.71842	−	0.216909i		0			−	1.66569i		0		−1.80300				0		2.90590	+	0.745480i		0
533.3		0		−1.71470	+	0.244568i		0			−	3.20130i		0		1.89175				0		2.88037	−	0.838721i		0
533.4		0		−1.69913	−	0.336113i		0				3.14143i		0		1.79813				0		2.77406	+	1.14220i		0
533.5		0		−1.67722	−	0.432364i		0				3.09919i		0		−3.82729				0		2.62612	+	1.45034i		0
533.6		0		−1.62308	+	0.604667i		0			−	0.548352i		0		−3.70356				0		2.26875	−	1.96284i		0
533.7		0		−1.25089	−	1.19803i		0			−	1.87331i		0		2.25590				0		0.129430	+	2.99721i		0
533.8		0		−1.24989	+	1.19908i		0				2.12266i		0		3.66376				0		0.124426	−	2.99742i		0
533.9		0		−1.14342	+	1.30099i		0				2.35324i		0		0.681957				0		−0.385175	−	2.97517i		0
533.10		0		−1.14059	−	1.30348i		0				1.82246i		0		−0.0158758				0		−0.398121	+	2.97347i		0
533.11		0		−1.07060	+	1.36155i		0			−	1.13120i		0		−3.35679				0		−0.707611	−	2.91535i		0
533.12		0		−0.786089	−	1.54339i		0			−	2.25557i		0		1.55772				0		−1.76413	+	2.42649i		0
533.13		0		−0.533930	−	1.64770i		0				1.53480i		0		−1.94130				0		−2.42984	+	1.75952i		0
533.14		0		−0.142707	+	1.72616i		0			−	1.26473i		0		3.70810				0		−2.95927	−	0.492672i		0
533.15		0		0.0971346	−	1.72932i		0				4.44588i		0		4.77144				0		−2.98113	−	0.335954i		0
533.16		0		0.157232	+	1.72490i		0			−	0.558390i		0		−1.35163				0		−2.95056	+	0.542418i		0
533.17		0		0.173243	+	1.72336i		0				3.25668i		0		−1.51033				0		−2.93997	+	0.597122i		0
533.18		0		0.273459	+	1.71033i		0			−	3.63397i		0		−2.35733				0		−2.85044	+	0.935407i		0
533.19		0		0.321336	−	1.70198i		0				0.618324i		0		−0.517164				0		−2.79349	−	1.09382i		0
533.20		0		0.361301	−	1.69395i		0			−	2.93503i		0		−3.63855				0		−2.73892	−	1.22405i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
279.o	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1116.2.p.a	✓	64
3.b	odd	2	1		3348.2.p.a		64
9.c	even	3	1		3348.2.bf.a		64
9.d	odd	6	1		1116.2.bf.a	yes	64
31.e	odd	6	1		1116.2.bf.a	yes	64
93.g	even	6	1		3348.2.bf.a		64
279.n	odd	6	1		3348.2.p.a		64
279.o	even	6	1	inner	1116.2.p.a	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1116.2.p.a	✓	64	1.a	even	1	1	trivial
1116.2.p.a	✓	64	279.o	even	6	1	inner
1116.2.bf.a	yes	64	9.d	odd	6	1
1116.2.bf.a	yes	64	31.e	odd	6	1
3348.2.p.a		64	3.b	odd	2	1
3348.2.p.a		64	279.n	odd	6	1
3348.2.bf.a		64	9.c	even	3	1
3348.2.bf.a		64	93.g	even	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1116, [\chi])\).