Newform orbit 2448.2.be.j

• Label: 2448.2.be.j
• Level: $2448$
• Weight: $2$
• Character orbit: 2448.be
• Analytic conductor: $19.547$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2448.be (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(19.5473784148\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{-1}) \)
Defining polynomial:	\( x^{2} + 1 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 34)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(i = \sqrt{-1}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q + (i + 1) q^{5}+O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{5}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2448\mathbb{Z}\right)^\times\).

\(n\)	\(613\)	\(1361\)	\(1873\)	\(2143\)
\(\chi(n)\)	\(1\)	\(1\)	\(i\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1441.1

		1.00000i
	−	1.00000i

0

0

0

1.00000

+

1.00000i

0

0

0

0

0

1585.1

0

0

0

1.00000

−

1.00000i

0

0

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
17.c	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2448.2.be.j		2
3.b	odd	2	1		272.2.o.c		2
4.b	odd	2	1		306.2.g.d		2
12.b	even	2	1		34.2.c.b	✓	2
17.c	even	4	1	inner	2448.2.be.j		2
24.f	even	2	1		1088.2.o.k		2
24.h	odd	2	1		1088.2.o.i		2
51.f	odd	4	1		272.2.o.c		2
51.g	odd	8	2		4624.2.a.l		2
60.h	even	2	1		850.2.h.c		2
60.l	odd	4	1		850.2.g.a		2
60.l	odd	4	1		850.2.g.d		2
68.f	odd	4	1		306.2.g.d		2
68.g	odd	8	2		5202.2.a.bb		2
204.h	even	2	1		578.2.c.b		2
204.l	even	4	1		34.2.c.b	✓	2
204.l	even	4	1		578.2.c.b		2
204.p	even	8	2		578.2.a.b		2
204.p	even	8	2		578.2.b.c		2
204.t	odd	16	8		578.2.d.f		8
408.q	even	4	1		1088.2.o.k		2
408.t	odd	4	1		1088.2.o.i		2
1020.q	odd	4	1		850.2.g.a		2
1020.ba	even	4	1		850.2.h.c		2
1020.bl	odd	4	1		850.2.g.d		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
34.2.c.b	✓	2	12.b	even	2	1
34.2.c.b	✓	2	204.l	even	4	1
272.2.o.c		2	3.b	odd	2	1
272.2.o.c		2	51.f	odd	4	1
306.2.g.d		2	4.b	odd	2	1
306.2.g.d		2	68.f	odd	4	1
578.2.a.b		2	204.p	even	8	2
578.2.b.c		2	204.p	even	8	2
578.2.c.b		2	204.h	even	2	1
578.2.c.b		2	204.l	even	4	1
578.2.d.f		8	204.t	odd	16	8
850.2.g.a		2	60.l	odd	4	1
850.2.g.a		2	1020.q	odd	4	1
850.2.g.d		2	60.l	odd	4	1
850.2.g.d		2	1020.bl	odd	4	1
850.2.h.c		2	60.h	even	2	1
850.2.h.c		2	1020.ba	even	4	1
1088.2.o.i		2	24.h	odd	2	1
1088.2.o.i		2	408.t	odd	4	1
1088.2.o.k		2	24.f	even	2	1
1088.2.o.k		2	408.q	even	4	1
2448.2.be.j		2	1.a	even	1	1	trivial
2448.2.be.j		2	17.c	even	4	1	inner
4624.2.a.l		2	51.g	odd	8	2
5202.2.a.bb		2	68.g	odd	8	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(2448, [\chi])\):

\( T_{5}^{2} - 2T_{5} + 2 \)

\( T_{7} \)

\( T_{11}^{2} + 8T_{11} + 32 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} \)
$5$	\( T^{2} - 2T + 2 \)
$7$	\( T^{2} \)
$11$	\( T^{2} + 8T + 32 \)