Newform orbit 5472.2.j.d

• Label: 5472.2.j.d
• Level: $5472$
• Weight: $2$
• Character orbit: 5472.j
• Analytic conductor: $43.694$
• Analytic rank: $0$
• Dimension: $36$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5472.j (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(43.6941399860\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Twist minimal:	no (minimal twist has level 1368)
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.

\(\operatorname{Tr}(f)(q) = \) \( 36 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4751.1		0			0			0		−4.36981				0				4.25041i		0			0			0
4751.2		0			0			0		−4.36981				0			−	4.25041i		0			0			0
4751.3		0			0			0		−3.32299				0			−	1.97397i		0			0			0
4751.4		0			0			0		−3.32299				0				1.97397i		0			0			0
4751.5		0			0			0		−3.05234				0			−	3.72881i		0			0			0
4751.6		0			0			0		−3.05234				0				3.72881i		0			0			0
4751.7		0			0			0		−2.93803				0				2.58934i		0			0			0
4751.8		0			0			0		−2.93803				0			−	2.58934i		0			0			0
4751.9		0			0			0		−1.93540				0				0.0837338i		0			0			0
4751.10		0			0			0		−1.93540				0			−	0.0837338i		0			0			0
4751.11		0			0			0		−1.14810				0				1.48532i		0			0			0
4751.12		0			0			0		−1.14810				0			−	1.48532i		0			0			0
4751.13		0			0			0		−0.723173				0			−	5.08024i		0			0			0
4751.14		0			0			0		−0.723173				0				5.08024i		0			0			0
4751.15		0			0			0		−0.534664				0			−	0.617346i		0			0			0
4751.16		0			0			0		−0.534664				0				0.617346i		0			0			0
4751.17		0			0			0		−0.202245				0			−	1.01271i		0			0			0
4751.18		0			0			0		−0.202245				0				1.01271i		0			0			0
4751.19		0			0			0		0.202245				0			−	1.01271i		0			0			0
4751.20		0			0			0		0.202245				0				1.01271i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
8.d	odd	2	1	inner
24.f	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	5472.2.j.d		36
3.b	odd	2	1	inner	5472.2.j.d		36
4.b	odd	2	1		1368.2.j.d	✓	36
8.b	even	2	1		1368.2.j.d	✓	36
8.d	odd	2	1	inner	5472.2.j.d		36
12.b	even	2	1		1368.2.j.d	✓	36
24.f	even	2	1	inner	5472.2.j.d		36
24.h	odd	2	1		1368.2.j.d	✓	36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1368.2.j.d	✓	36	4.b	odd	2	1
1368.2.j.d	✓	36	8.b	even	2	1
1368.2.j.d	✓	36	12.b	even	2	1
1368.2.j.d	✓	36	24.h	odd	2	1
5472.2.j.d		36	1.a	even	1	1	trivial
5472.2.j.d		36	3.b	odd	2	1	inner
5472.2.j.d		36	8.d	odd	2	1	inner
5472.2.j.d		36	24.f	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^18 - 54*T5^16 + 1126*T5^14 - 11588*T5^12 + 61761*T5^10 - 163094*T5^8 + 192396*T5^6 - 92744*T5^4 + 16000*T5^2 - 512