Newform orbit 288.2.v.c

• Label: 288.2.v.c
• Level: $288$
• Weight: $2$
• Character orbit: 288.v
• Analytic conductor: $2.300$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.v (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.29969157821\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(8\) over \(\Q(\zeta_{8})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

$q$-expansion

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

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
37.1	−1.41364	−	0.0402136i		0		1.99677	+	0.113695i	−1.51282	−	0.626632i		0		−1.32530	−	1.32530i	−2.81814	−	0.241022i		0		2.11339	+	0.946670i
37.2	−1.06920	+	0.925636i		0		0.286395	−	1.97939i	3.41317	+	1.41378i		0		−1.42999	−	1.42999i	1.52598	+	2.38147i		0		−4.95802	+	1.64773i
37.3	−0.835415	−	1.14109i		0		−0.604162	+	1.90656i	−0.823699	−	0.341187i		0		0.760681	+	0.760681i	2.68028	−	0.903371i		0		0.298806	+	1.22495i
37.4	−0.716976	+	1.21899i		0		−0.971891	−	1.74798i	−2.42249	−	1.00343i		0		3.40882	+	3.40882i	2.82760	+	0.0685293i		0		2.96004	−	2.23356i
37.5	0.716976	−	1.21899i		0		−0.971891	−	1.74798i	2.42249	+	1.00343i		0		3.40882	+	3.40882i	−2.82760	−	0.0685293i		0		2.96004	−	2.23356i
37.6	0.835415	+	1.14109i		0		−0.604162	+	1.90656i	0.823699	+	0.341187i		0		0.760681	+	0.760681i	−2.68028	+	0.903371i		0		0.298806	+	1.22495i
37.7	1.06920	−	0.925636i		0		0.286395	−	1.97939i	−3.41317	−	1.41378i		0		−1.42999	−	1.42999i	−1.52598	−	2.38147i		0		−4.95802	+	1.64773i
37.8	1.41364	+	0.0402136i		0		1.99677	+	0.113695i	1.51282	+	0.626632i		0		−1.32530	−	1.32530i	2.81814	+	0.241022i		0		2.11339	+	0.946670i
109.1	−1.41364	+	0.0402136i		0		1.99677	−	0.113695i	−1.51282	+	0.626632i		0		−1.32530	+	1.32530i	−2.81814	+	0.241022i		0		2.11339	−	0.946670i
109.2	−1.06920	−	0.925636i		0		0.286395	+	1.97939i	3.41317	−	1.41378i		0		−1.42999	+	1.42999i	1.52598	−	2.38147i		0		−4.95802	−	1.64773i
109.3	−0.835415	+	1.14109i		0		−0.604162	−	1.90656i	−0.823699	+	0.341187i		0		0.760681	−	0.760681i	2.68028	+	0.903371i		0		0.298806	−	1.22495i
109.4	−0.716976	−	1.21899i		0		−0.971891	+	1.74798i	−2.42249	+	1.00343i		0		3.40882	−	3.40882i	2.82760	−	0.0685293i		0		2.96004	+	2.23356i
109.5	0.716976	+	1.21899i		0		−0.971891	+	1.74798i	2.42249	−	1.00343i		0		3.40882	−	3.40882i	−2.82760	+	0.0685293i		0		2.96004	+	2.23356i
109.6	0.835415	−	1.14109i		0		−0.604162	−	1.90656i	0.823699	−	0.341187i		0		0.760681	−	0.760681i	−2.68028	−	0.903371i		0		0.298806	−	1.22495i
109.7	1.06920	+	0.925636i		0		0.286395	+	1.97939i	−3.41317	+	1.41378i		0		−1.42999	+	1.42999i	−1.52598	+	2.38147i		0		−4.95802	−	1.64773i
109.8	1.41364	−	0.0402136i		0		1.99677	−	0.113695i	1.51282	−	0.626632i		0		−1.32530	+	1.32530i	2.81814	−	0.241022i		0		2.11339	−	0.946670i
181.1	−1.39967	−	0.202304i		0		1.91815	+	0.566318i	1.53803	−	3.71314i		0		−1.56292	−	1.56292i	−2.57020	−	1.18071i		0		−2.90392	+	4.88602i
181.2	−1.14926	+	0.824131i		0		0.641617	−	1.89429i	−0.549515	+	1.32665i		0		0.197478	+	0.197478i	0.823754	+	2.70581i		0		−0.461792	−	1.97754i
181.3	−0.582293	−	1.28877i		0		−1.32187	+	1.50089i	0.445570	−	1.07570i		0		2.57533	+	2.57533i	2.70402	+	0.829636i		0		−1.64578	+	0.0521344i
181.4	−0.165832	+	1.40446i		0		−1.94500	−	0.465809i	0.805403	−	1.94441i		0		−2.62411	−	2.62411i	0.976752	−	2.65442i		0		2.59728	+	1.45360i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
32.g	even	8	1	inner
96.p	odd	8	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	288.2.v.c	✓	32
3.b	odd	2	1	inner	288.2.v.c	✓	32
4.b	odd	2	1		1152.2.v.d		32
12.b	even	2	1		1152.2.v.d		32
32.g	even	8	1	inner	288.2.v.c	✓	32
32.h	odd	8	1		1152.2.v.d		32
96.o	even	8	1		1152.2.v.d		32
96.p	odd	8	1	inner	288.2.v.c	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
288.2.v.c	✓	32	1.a	even	1	1	trivial
288.2.v.c	✓	32	3.b	odd	2	1	inner
288.2.v.c	✓	32	32.g	even	8	1	inner
288.2.v.c	✓	32	96.p	odd	8	1	inner
1152.2.v.d		32	4.b	odd	2	1
1152.2.v.d		32	12.b	even	2	1
1152.2.v.d		32	32.h	odd	8	1
1152.2.v.d		32	96.o	even	8	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^32 - 672*T5^26 + 52736*T5^24 - 173184*T5^22 + 225792*T5^20 + 4564224*T5^18 + 45936768*T5^16 - 7729152*T5^14 + 21823488*T5^12 + 344365056*T5^10 + 1756430336*T5^8 + 1116364800*T5^6 + 184320000*T5^4 - 768000000*T5^2 + 1600000000