Newform orbit 1152.2.v.d

• Label: 1152.2.v.d
• Level: $1152$
• Weight: $2$
• Character orbit: 1152.v
• Analytic conductor: $9.199$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.v (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.19876631285\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(8\) over \(\Q(\zeta_{8})\)
Twist minimal:	no (minimal twist has level 288)
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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
145.1		0			0			0		−3.41317	+	1.41378i		0		1.42999	−	1.42999i		0			0			0
145.2		0			0			0		−2.42249	+	1.00343i		0		−3.40882	+	3.40882i		0			0			0
145.3		0			0			0		−1.51282	+	0.626632i		0		1.32530	−	1.32530i		0			0			0
145.4		0			0			0		−0.823699	+	0.341187i		0		−0.760681	+	0.760681i		0			0			0
145.5		0			0			0		0.823699	−	0.341187i		0		−0.760681	+	0.760681i		0			0			0
145.6		0			0			0		1.51282	−	0.626632i		0		1.32530	−	1.32530i		0			0			0
145.7		0			0			0		2.42249	−	1.00343i		0		−3.40882	+	3.40882i		0			0			0
145.8		0			0			0		3.41317	−	1.41378i		0		1.42999	−	1.42999i		0			0			0
433.1		0			0			0		−1.53803	+	3.71314i		0		1.56292	+	1.56292i		0			0			0
433.2		0			0			0		−0.805403	+	1.94441i		0		2.62411	+	2.62411i		0			0			0
433.3		0			0			0		−0.549515	+	1.32665i		0		−0.197478	−	0.197478i		0			0			0
433.4		0			0			0		−0.445570	+	1.07570i		0		−2.57533	−	2.57533i		0			0			0
433.5		0			0			0		0.445570	−	1.07570i		0		−2.57533	−	2.57533i		0			0			0
433.6		0			0			0		0.549515	−	1.32665i		0		−0.197478	−	0.197478i		0			0			0
433.7		0			0			0		0.805403	−	1.94441i		0		2.62411	+	2.62411i		0			0			0
433.8		0			0			0		1.53803	−	3.71314i		0		1.56292	+	1.56292i		0			0			0
721.1		0			0			0		−1.53803	−	3.71314i		0		1.56292	−	1.56292i		0			0			0
721.2		0			0			0		−0.805403	−	1.94441i		0		2.62411	−	2.62411i		0			0			0
721.3		0			0			0		−0.549515	−	1.32665i		0		−0.197478	+	0.197478i		0			0			0
721.4		0			0			0		−0.445570	−	1.07570i		0		−2.57533	+	2.57533i		0			0			0

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	1152.2.v.d		32
3.b	odd	2	1	inner	1152.2.v.d		32
4.b	odd	2	1		288.2.v.c	✓	32
12.b	even	2	1		288.2.v.c	✓	32
32.g	even	8	1	inner	1152.2.v.d		32
32.h	odd	8	1		288.2.v.c	✓	32
96.o	even	8	1		288.2.v.c	✓	32
96.p	odd	8	1	inner	1152.2.v.d		32

    

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

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