Newform orbit 3648.2.e.c

• Label: 3648.2.e.c
• Level: $3648$
• Weight: $2$
• Character orbit: 3648.e
• Analytic conductor: $29.129$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3648 = 2^{6} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3648.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(29.1294266574\)
Analytic rank:	\(0\)
Dimension:	\(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 28 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
607.1		0			−	1.00000i		0			−	3.98623i		0				2.46603i		0		−1.00000				0
607.2		0			−	1.00000i		0			−	2.63277i		0			−	1.34585i		0		−1.00000				0
607.3		0			−	1.00000i		0			−	2.38601i		0			−	4.23774i		0		−1.00000				0
607.4		0			−	1.00000i		0			−	2.20976i		0				4.06668i		0		−1.00000				0
607.5		0			−	1.00000i		0			−	1.33030i		0				3.22149i		0		−1.00000				0
607.6		0			−	1.00000i		0			−	1.32356i		0				1.08022i		0		−1.00000				0
607.7		0			−	1.00000i		0			−	0.284443i		0			−	2.25083i		0		−1.00000				0
607.8		0			−	1.00000i		0				0.284443i		0			−	2.25083i		0		−1.00000				0
607.9		0			−	1.00000i		0				1.32356i		0				1.08022i		0		−1.00000				0
607.10		0			−	1.00000i		0				1.33030i		0				3.22149i		0		−1.00000				0
607.11		0			−	1.00000i		0				2.20976i		0				4.06668i		0		−1.00000				0
607.12		0			−	1.00000i		0				2.38601i		0			−	4.23774i		0		−1.00000				0
607.13		0			−	1.00000i		0				2.63277i		0			−	1.34585i		0		−1.00000				0
607.14		0			−	1.00000i		0				3.98623i		0				2.46603i		0		−1.00000				0
607.15		0				1.00000i		0			−	3.98623i		0			−	2.46603i		0		−1.00000				0
607.16		0				1.00000i		0			−	2.63277i		0				1.34585i		0		−1.00000				0
607.17		0				1.00000i		0			−	2.38601i		0				4.23774i		0		−1.00000				0
607.18		0				1.00000i		0			−	2.20976i		0			−	4.06668i		0		−1.00000				0
607.19		0				1.00000i		0			−	1.33030i		0			−	3.22149i		0		−1.00000				0
607.20		0				1.00000i		0			−	1.32356i		0			−	1.08022i		0		−1.00000				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
152.b	even	2	1	inner
152.g	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3648.2.e.c	✓	28
4.b	odd	2	1	inner	3648.2.e.c	✓	28
8.b	even	2	1		3648.2.e.d	yes	28
8.d	odd	2	1		3648.2.e.d	yes	28
19.b	odd	2	1		3648.2.e.d	yes	28
76.d	even	2	1		3648.2.e.d	yes	28
152.b	even	2	1	inner	3648.2.e.c	✓	28
152.g	odd	2	1	inner	3648.2.e.c	✓	28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
3648.2.e.c	✓	28	1.a	even	1	1	trivial
3648.2.e.c	✓	28	4.b	odd	2	1	inner
3648.2.e.c	✓	28	152.b	even	2	1	inner
3648.2.e.c	✓	28	152.g	odd	2	1	inner
3648.2.e.d	yes	28	8.b	even	2	1
3648.2.e.d	yes	28	8.d	odd	2	1
3648.2.e.d	yes	28	19.b	odd	2	1
3648.2.e.d	yes	28	76.d	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(3648, [\chi])\):

\( T_{5}^{14} + 37T_{5}^{12} + 503T_{5}^{10} + 3279T_{5}^{8} + 10836T_{5}^{6} + 17216T_{5}^{4} + 10816T_{5}^{2} + 768 \)

\( T_{13}^{7} + 6T_{13}^{6} - 40T_{13}^{5} - 216T_{13}^{4} + 560T_{13}^{3} + 1920T_{13}^{2} - 3328T_{13} - 256 \)