Newform orbit 264.3.e.a

• Label: 264.3.e.a
• Level: $264$
• Weight: $3$
• Character orbit: 264.e
• Analytic conductor: $7.193$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	264.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.19347897911\)
Analytic rank:	\(0\)
Dimension:	\(48\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 12 q^{4} - 144 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
109.1	−1.98900	−	0.209509i		−	1.73205i	3.91221	+	0.833424i			4.86020i	−0.362880	+	3.44504i			11.9744i	−7.60677	−	2.47732i	−3.00000			1.01825	−	9.66691i
109.2	−1.98900	+	0.209509i			1.73205i	3.91221	−	0.833424i		−	4.86020i	−0.362880	−	3.44504i		−	11.9744i	−7.60677	+	2.47732i	−3.00000			1.01825	+	9.66691i
109.3	−1.97091	−	0.339898i		−	1.73205i	3.76894	+	1.33981i		−	7.77788i	−0.588720	+	3.41371i		−	3.49979i	−6.97282	−	3.92170i	−3.00000			−2.64368	+	15.3295i
109.4	−1.97091	+	0.339898i			1.73205i	3.76894	−	1.33981i			7.77788i	−0.588720	−	3.41371i			3.49979i	−6.97282	+	3.92170i	−3.00000			−2.64368	−	15.3295i
109.5	−1.91114	−	0.589527i		−	1.73205i	3.30491	+	2.25334i			5.58827i	−1.02109	+	3.31019i		−	6.49360i	−4.98775	−	6.25479i	−3.00000			3.29444	−	10.6800i
109.6	−1.91114	+	0.589527i			1.73205i	3.30491	−	2.25334i		−	5.58827i	−1.02109	−	3.31019i			6.49360i	−4.98775	+	6.25479i	−3.00000			3.29444	+	10.6800i
109.7	−1.87221	−	0.703429i			1.73205i	3.01038	+	2.63394i			1.59860i	1.21837	−	3.24277i		−	6.07968i	−3.78328	−	7.04889i	−3.00000			1.12450	−	2.99291i
109.8	−1.87221	+	0.703429i		−	1.73205i	3.01038	−	2.63394i		−	1.59860i	1.21837	+	3.24277i			6.07968i	−3.78328	+	7.04889i	−3.00000			1.12450	+	2.99291i
109.9	−1.48334	−	1.34153i			1.73205i	0.400600	+	3.97989i			5.07502i	2.32360	−	2.56922i			3.53186i	4.74491	−	6.44095i	−3.00000			6.80828	−	7.52798i
109.10	−1.48334	+	1.34153i		−	1.73205i	0.400600	−	3.97989i		−	5.07502i	2.32360	+	2.56922i		−	3.53186i	4.74491	+	6.44095i	−3.00000			6.80828	+	7.52798i
109.11	−1.37848	−	1.44906i		−	1.73205i	−0.199564	+	3.99502i			0.815967i	−2.50985	+	2.38760i		−	6.88302i	6.06413	−	5.21789i	−3.00000			1.18239	−	1.12480i
109.12	−1.37848	+	1.44906i			1.73205i	−0.199564	−	3.99502i		−	0.815967i	−2.50985	−	2.38760i			6.88302i	6.06413	+	5.21789i	−3.00000			1.18239	+	1.12480i
109.13	−1.20499	−	1.59624i		−	1.73205i	−1.09598	+	3.84692i		−	3.79214i	−2.76477	+	2.08711i			12.8657i	7.46127	−	2.88607i	−3.00000			−6.05318	+	4.56951i
109.14	−1.20499	+	1.59624i			1.73205i	−1.09598	−	3.84692i			3.79214i	−2.76477	−	2.08711i		−	12.8657i	7.46127	+	2.88607i	−3.00000			−6.05318	−	4.56951i
109.15	−0.903479	−	1.78430i			1.73205i	−2.36745	+	3.22415i		−	1.33840i	3.09050	−	1.56487i		−	4.65928i	7.89180	+	1.31129i	−3.00000			−2.38810	+	1.20921i
109.16	−0.903479	+	1.78430i		−	1.73205i	−2.36745	−	3.22415i			1.33840i	3.09050	+	1.56487i			4.65928i	7.89180	−	1.31129i	−3.00000			−2.38810	−	1.20921i
109.17	−0.778275	−	1.84236i			1.73205i	−2.78858	+	2.86773i		−	8.51546i	3.19106	−	1.34801i			6.20652i	7.45366	+	2.90568i	−3.00000			−15.6885	+	6.62737i
109.18	−0.778275	+	1.84236i		−	1.73205i	−2.78858	−	2.86773i			8.51546i	3.19106	+	1.34801i		−	6.20652i	7.45366	−	2.90568i	−3.00000			−15.6885	−	6.62737i
109.19	−0.613981	−	1.90343i		−	1.73205i	−3.24605	+	2.33733i			6.76747i	−3.29683	+	1.06345i		−	3.01291i	6.44196	+	4.74354i	−3.00000			12.8814	−	4.15510i
109.20	−0.613981	+	1.90343i			1.73205i	−3.24605	−	2.33733i		−	6.76747i	−3.29683	−	1.06345i			3.01291i	6.44196	−	4.74354i	−3.00000			12.8814	+	4.15510i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.b	even	2	1	inner
11.b	odd	2	1	inner
88.b	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	264.3.e.a	✓	48
4.b	odd	2	1		1056.3.e.a		48
8.b	even	2	1	inner	264.3.e.a	✓	48
8.d	odd	2	1		1056.3.e.a		48
11.b	odd	2	1	inner	264.3.e.a	✓	48
44.c	even	2	1		1056.3.e.a		48
88.b	odd	2	1	inner	264.3.e.a	✓	48
88.g	even	2	1		1056.3.e.a		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
264.3.e.a	✓	48	1.a	even	1	1	trivial
264.3.e.a	✓	48	8.b	even	2	1	inner
264.3.e.a	✓	48	11.b	odd	2	1	inner
264.3.e.a	✓	48	88.b	odd	2	1	inner
1056.3.e.a		48	4.b	odd	2	1
1056.3.e.a		48	8.d	odd	2	1
1056.3.e.a		48	44.c	even	2	1
1056.3.e.a		48	88.g	even	2	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(264, [\chi])\).