Newform orbit 2736.3.b.e

• Label: 2736.3.b.e
• Level: $2736$
• Weight: $3$
• Character orbit: 2736.b
• Analytic conductor: $74.551$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2736.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(74.5506003290\)
Analytic rank:	\(0\)
Dimension:	\(32\)
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.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2735.1		0			0			0			−	6.53962i		0			−	7.08397i		0			0			0
2735.2		0			0			0				6.53962i		0				7.08397i		0			0			0
2735.3		0			0			0			−	1.26257i		0			−	8.06963i		0			0			0
2735.4		0			0			0				1.26257i		0				8.06963i		0			0			0
2735.5		0			0			0			−	6.53962i		0				7.08397i		0			0			0
2735.6		0			0			0				6.53962i		0			−	7.08397i		0			0			0
2735.7		0			0			0			−	1.26257i		0				8.06963i		0			0			0
2735.8		0			0			0				1.26257i		0			−	8.06963i		0			0			0
2735.9		0			0			0			−	1.26257i		0				8.06963i		0			0			0
2735.10		0			0			0				1.26257i		0			−	8.06963i		0			0			0
2735.11		0			0			0			−	5.60057i		0			−	2.03549i		0			0			0
2735.12		0			0			0				5.60057i		0				2.03549i		0			0			0
2735.13		0			0			0			−	6.53962i		0			−	7.08397i		0			0			0
2735.14		0			0			0				6.53962i		0				7.08397i		0			0			0
2735.15		0			0			0			−	5.60057i		0			−	2.03549i		0			0			0
2735.16		0			0			0				5.60057i		0				2.03549i		0			0			0
2735.17		0			0			0			−	5.60057i		0				2.03549i		0			0			0
2735.18		0			0			0				5.60057i		0			−	2.03549i		0			0			0
2735.19		0			0			0			−	5.60057i		0				2.03549i		0			0			0
2735.20		0			0			0				5.60057i		0			−	2.03549i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
4.b	odd	2	1	inner
12.b	even	2	1	inner
19.b	odd	2	1	inner
57.d	even	2	1	inner
76.d	even	2	1	inner
228.b	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2736.3.b.e	✓	32
3.b	odd	2	1	inner	2736.3.b.e	✓	32
4.b	odd	2	1	inner	2736.3.b.e	✓	32
12.b	even	2	1	inner	2736.3.b.e	✓	32
19.b	odd	2	1	inner	2736.3.b.e	✓	32
57.d	even	2	1	inner	2736.3.b.e	✓	32
76.d	even	2	1	inner	2736.3.b.e	✓	32
228.b	odd	2	1	inner	2736.3.b.e	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2736.3.b.e	✓	32	1.a	even	1	1	trivial
2736.3.b.e	✓	32	3.b	odd	2	1	inner
2736.3.b.e	✓	32	4.b	odd	2	1	inner
2736.3.b.e	✓	32	12.b	even	2	1	inner
2736.3.b.e	✓	32	19.b	odd	2	1	inner
2736.3.b.e	✓	32	57.d	even	2	1	inner
2736.3.b.e	✓	32	76.d	even	2	1	inner
2736.3.b.e	✓	32	228.b	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{8} + 88T_{5}^{6} + 2389T_{5}^{4} + 20052T_{5}^{2} + 26244 \) acting on \(S_{3}^{\mathrm{new}}(2736, [\chi])\).