Newform orbit 2448.2.a.y

• Label: 2448.2.a.y
• Level: $2448$
• Weight: $2$
• Character orbit: 2448.a
• Self dual: yes
• Analytic conductor: $19.547$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$2448 = 2^{4} \cdot 3^{2} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	2448.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$19.5473784148$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{3})$
Defining polynomial:	$x^{2} - 3$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 68)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the $q$-expansion are expressed in terms of $\beta = \sqrt{3}$. We also show the integral $q$-expansion of the trace form.

$f(q)$	$=$	q + 2*b * q^5 + (b + 1) * q^7 + (b - 3) * q^11 + (2*b + 2) * q^13 + q^17 + (2*b - 2) * q^19 + (b - 3) * q^23 + 7 * q^25 - 2*b * q^29 + (-3*b + 1) * q^31 + (2*b + 6) * q^35 + (-2*b + 8) * q^37 + 6 * q^41 + (6*b - 2) * q^43 - 4*b * q^47 + (2*b - 3) * q^49 + (-4*b - 6) * q^53 + (-6*b + 6) * q^55 + (-2*b + 6) * q^59 + (2*b - 4) * q^61 + (4*b + 12) * q^65 + (-4*b - 8) * q^67 + (-3*b - 3) * q^71 + 2 * q^73 - 2*b * q^77 + (3*b + 7) * q^79 + (2*b - 6) * q^83 + 2*b * q^85 + (2*b - 6) * q^89 + (4*b + 8) * q^91 + (-4*b + 12) * q^95 + (-4*b + 2) * q^97
$\operatorname{Tr}(f)(q)$	$=$	2 * q + 2 * q^7 - 6 * q^11 + 4 * q^13 + 2 * q^17 - 4 * q^19 - 6 * q^23 + 14 * q^25 + 2 * q^31 + 12 * q^35 + 16 * q^37 + 12 * q^41 - 4 * q^43 - 6 * q^49 - 12 * q^53 + 12 * q^55 + 12 * q^59 - 8 * q^61 + 24 * q^65 - 16 * q^67 - 6 * q^71 + 4 * q^73 + 14 * q^79 - 12 * q^83 - 12 * q^89 + 16 * q^91 + 24 * q^95 + 4 * q^97

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

1.1

−1.73205
1.73205

0

0

0

−3.46410

0

−0.732051

0

0

0

1.2

0

0

0

3.46410

0

2.73205

0

0

0

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$-1$
$17$	$-1$

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2448.2.a.y		2
3.b	odd	2	1		272.2.a.e		2
4.b	odd	2	1		612.2.a.e		2
8.b	even	2	1		9792.2.a.cs		2
8.d	odd	2	1		9792.2.a.cr		2
12.b	even	2	1		68.2.a.a	✓	2
15.d	odd	2	1		6800.2.a.bh		2
24.f	even	2	1		1088.2.a.p		2
24.h	odd	2	1		1088.2.a.t		2
51.c	odd	2	1		4624.2.a.x		2
60.h	even	2	1		1700.2.a.d		2
60.l	odd	4	2		1700.2.e.c		4
84.h	odd	2	1		3332.2.a.h		2
132.d	odd	2	1		8228.2.a.k		2
204.h	even	2	1		1156.2.a.a		2
204.l	even	4	2		1156.2.b.c		4
204.p	even	8	4		1156.2.e.d		8
204.t	odd	16	8		1156.2.h.f		16

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
68.2.a.a	✓	2	12.b	even	2	1
272.2.a.e		2	3.b	odd	2	1
612.2.a.e		2	4.b	odd	2	1
1088.2.a.p		2	24.f	even	2	1
1088.2.a.t		2	24.h	odd	2	1
1156.2.a.a		2	204.h	even	2	1
1156.2.b.c		4	204.l	even	4	2
1156.2.e.d		8	204.p	even	8	4
1156.2.h.f		16	204.t	odd	16	8
1700.2.a.d		2	60.h	even	2	1
1700.2.e.c		4	60.l	odd	4	2
2448.2.a.y		2	1.a	even	1	1	trivial
3332.2.a.h		2	84.h	odd	2	1
4624.2.a.x		2	51.c	odd	2	1
6800.2.a.bh		2	15.d	odd	2	1
8228.2.a.k		2	132.d	odd	2	1
9792.2.a.cr		2	8.d	odd	2	1
9792.2.a.cs		2	8.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(2448))$:

$T_{5}^{2} - 12$

$T_{7}^{2} - 2T_{7} - 2$

$T_{11}^{2} + 6T_{11} + 6$

$T_{19}^{2} + 4T_{19} - 8$

$T_{23}^{2} + 6T_{23} + 6$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{2}$
$3$	$T^{2}$
$5$	$T^{2} - 12$
$7$	$T^{2} - 2T - 2$
$11$	$T^{2} + 6T + 6$