Newform orbit 648.5.e.c

• Label: 648.5.e.c
• Level: $648$
• Weight: $5$
• Character orbit: 648.e
• Analytic conductor: $66.984$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	648.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(66.9837360783\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
161.1		0			0			0			−	44.1416i		0		50.7573				0			0			0
161.2		0			0			0			−	42.1641i		0		27.1513				0			0			0
161.3		0			0			0			−	38.5341i		0		−90.7519				0			0			0
161.4		0			0			0			−	30.0060i		0		75.5106				0			0			0
161.5		0			0			0			−	26.6535i		0		−57.6696				0			0			0
161.6		0			0			0			−	24.0611i		0		−75.8370				0			0			0
161.7		0			0			0			−	23.5604i		0		−0.171936				0			0			0
161.8		0			0			0			−	21.8323i		0		−15.8757				0			0			0
161.9		0			0			0			−	16.9129i		0		85.9149				0			0			0
161.10		0			0			0			−	14.2460i		0		−23.1568				0			0			0
161.11		0			0			0			−	8.57576i		0		4.75224				0			0			0
161.12		0			0			0			−	2.20234i		0		19.3765				0			0			0
161.13		0			0			0				2.20234i		0		19.3765				0			0			0
161.14		0			0			0				8.57576i		0		4.75224				0			0			0
161.15		0			0			0				14.2460i		0		−23.1568				0			0			0
161.16		0			0			0				16.9129i		0		85.9149				0			0			0
161.17		0			0			0				21.8323i		0		−15.8757				0			0			0
161.18		0			0			0				23.5604i		0		−0.171936				0			0			0
161.19		0			0			0				24.0611i		0		−75.8370				0			0			0
161.20		0			0			0				26.6535i		0		−57.6696				0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	648.5.e.c		24
3.b	odd	2	1	inner	648.5.e.c		24
4.b	odd	2	1		1296.5.e.j		24
9.c	even	3	1		72.5.m.a	✓	24
9.c	even	3	1		216.5.m.a		24
9.d	odd	6	1		72.5.m.a	✓	24
9.d	odd	6	1		216.5.m.a		24
12.b	even	2	1		1296.5.e.j		24
36.f	odd	6	1		144.5.q.d		24
36.f	odd	6	1		432.5.q.d		24
36.h	even	6	1		144.5.q.d		24
36.h	even	6	1		432.5.q.d		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
72.5.m.a	✓	24	9.c	even	3	1
72.5.m.a	✓	24	9.d	odd	6	1
144.5.q.d		24	36.f	odd	6	1
144.5.q.d		24	36.h	even	6	1
216.5.m.a		24	9.c	even	3	1
216.5.m.a		24	9.d	odd	6	1
432.5.q.d		24	36.f	odd	6	1
432.5.q.d		24	36.h	even	6	1
648.5.e.c		24	1.a	even	1	1	trivial
648.5.e.c		24	3.b	odd	2	1	inner
1296.5.e.j		24	4.b	odd	2	1
1296.5.e.j		24	12.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 + 9000*T5^22 + 34761852*T5^20 + 75818127560*T5^18 + 103485321005382*T5^16 + 92587090619252520*T5^14 + 55232553000184837980*T5^12 + 21864368385355801132152*T5^10 + 5587231299483330677993985*T5^8 + 868176939348239278095669488*T5^6 + 72749465735704093202633343072*T5^4 + 2484637302227692831764365940480*T5^2 + 10435789190112251610840955404544