Newform orbit 5824.2.a.bl

• Label: 5824.2.a.bl
• Level: $5824$
• Weight: $2$
• Character orbit: 5824.a
• Self dual: yes
• Analytic conductor: $46.505$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$5824 = 2^{6} \cdot 7 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	5824.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$46.5048741372$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{2})$
Defining polynomial:	$x^{2} - 2$
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the $q$-expansion are expressed in terms of $\beta = \sqrt{2}$. We also show the integral $q$-expansion of the trace form.

$f(q)$	$=$	q + b * q^3 + (-b - 3) * q^5 + q^7 - q^9 + 3*b * q^11 + q^13 + (-3*b - 2) * q^15 - b * q^17 + (-3*b + 3) * q^19 + b * q^21 + (2*b - 3) * q^23 + (6*b + 6) * q^25 - 4*b * q^27 + (-2*b - 3) * q^29 + (-3*b - 1) * q^31 + 6 * q^33 + (-b - 3) * q^35 + (3*b + 2) * q^37 + b * q^39 + (-2*b + 6) * q^41 + 5 * q^43 + (b + 3) * q^45 + (b + 3) * q^47 + q^49 - 2 * q^51 + (2*b + 3) * q^53 + (-9*b - 6) * q^55 + (3*b - 6) * q^57 + (-4*b - 6) * q^59 - 6 * q^61 - q^63 + (-b - 3) * q^65 + (-6*b + 6) * q^67 + (-3*b + 4) * q^69 + (5*b - 6) * q^71 + (3*b - 5) * q^73 + (6*b + 12) * q^75 + 3*b * q^77 + (-6*b + 7) * q^79 - 5 * q^81 + (3*b - 9) * q^83 + (3*b + 2) * q^85 + (-3*b - 4) * q^87 + (b + 3) * q^89 + q^91 + (-b - 6) * q^93 + (6*b - 3) * q^95 + (-9*b - 1) * q^97 - 3*b * q^99
$\operatorname{Tr}(f)(q)$	$=$	2 * q - 6 * q^5 + 2 * q^7 - 2 * q^9 + 2 * q^13 - 4 * q^15 + 6 * q^19 - 6 * q^23 + 12 * q^25 - 6 * q^29 - 2 * q^31 + 12 * q^33 - 6 * q^35 + 4 * q^37 + 12 * q^41 + 10 * q^43 + 6 * q^45 + 6 * q^47 + 2 * q^49 - 4 * q^51 + 6 * q^53 - 12 * q^55 - 12 * q^57 - 12 * q^59 - 12 * q^61 - 2 * q^63 - 6 * q^65 + 12 * q^67 + 8 * q^69 - 12 * q^71 - 10 * q^73 + 24 * q^75 + 14 * q^79 - 10 * q^81 - 18 * q^83 + 4 * q^85 - 8 * q^87 + 6 * q^89 + 2 * q^91 - 12 * q^93 - 6 * q^95 - 2 * 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

−1.41421
1.41421

0

−1.41421

0

−1.58579

0

1.00000

0

−1.00000

0

1.2

0

1.41421

0

−4.41421

0

1.00000

0

−1.00000

0

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$7$	$-1$
$13$	$-1$

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	5824.2.a.bl		2
4.b	odd	2	1		5824.2.a.bk		2
8.b	even	2	1		91.2.a.c	✓	2
8.d	odd	2	1		1456.2.a.q		2
24.h	odd	2	1		819.2.a.h		2
40.f	even	2	1		2275.2.a.j		2
56.h	odd	2	1		637.2.a.g		2
56.j	odd	6	2		637.2.e.g		4
56.p	even	6	2		637.2.e.f		4
104.e	even	2	1		1183.2.a.d		2
104.j	odd	4	2		1183.2.c.d		4
168.i	even	2	1		5733.2.a.s		2
728.l	odd	2	1		8281.2.a.v		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
91.2.a.c	✓	2	8.b	even	2	1
637.2.a.g		2	56.h	odd	2	1
637.2.e.f		4	56.p	even	6	2
637.2.e.g		4	56.j	odd	6	2
819.2.a.h		2	24.h	odd	2	1
1183.2.a.d		2	104.e	even	2	1
1183.2.c.d		4	104.j	odd	4	2
1456.2.a.q		2	8.d	odd	2	1
2275.2.a.j		2	40.f	even	2	1
5733.2.a.s		2	168.i	even	2	1
5824.2.a.bk		2	4.b	odd	2	1
5824.2.a.bl		2	1.a	even	1	1	trivial
8281.2.a.v		2	728.l	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(5824))$:

$T_{3}^{2} - 2$

$T_{5}^{2} + 6T_{5} + 7$

$T_{11}^{2} - 18$

$T_{17}^{2} - 2$

$T_{19}^{2} - 6T_{19} - 9$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{2}$
$3$	$T^{2} - 2$
$5$	$T^{2} + 6T + 7$
$7$	$(T - 1)^{2}$
$11$	$T^{2} - 18$