Newform orbit 5850.2.a.cg

• Label: 5850.2.a.cg
• Level: $5850$
• Weight: $2$
• Character orbit: 5850.a
• Self dual: yes
• Analytic conductor: $46.712$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	5850.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$46.7124851824$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{41})$
Defining polynomial:	$x^{2} - x - 10$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 1950)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the $q$-expansion are expressed in terms of $\beta = \frac{1}{2}(1 + \sqrt{41})$. We also show the integral $q$-expansion of the trace form.

$f(q)$	$=$	q - q^2 + q^4 + (b + 1) * q^7 - q^8 + (-b - 1) * q^11 - q^13 + (-b - 1) * q^14 + q^16 + (b - 3) * q^17 + (-b + 2) * q^19 + (b + 1) * q^22 + q^26 + (b + 1) * q^28 + (2*b - 1) * q^29 + (-3*b + 1) * q^31 - q^32 + (-b + 3) * q^34 + (-b + 2) * q^37 + (b - 2) * q^38 + b * q^41 + (-2*b - 4) * q^43 + (-b - 1) * q^44 - 7 * q^47 + (3*b + 4) * q^49 - q^52 + (-2*b + 5) * q^53 + (-b - 1) * q^56 + (-2*b + 1) * q^58 + (-b + 1) * q^59 + (3*b + 3) * q^61 + (3*b - 1) * q^62 + q^64 + (-2*b + 1) * q^67 + (b - 3) * q^68 + (b - 2) * q^71 - 12 * q^73 + (b - 2) * q^74 + (-b + 2) * q^76 + (-3*b - 11) * q^77 + (-b - 2) * q^79 - b * q^82 + (b + 7) * q^83 + (2*b + 4) * q^86 + (b + 1) * q^88 + (-2*b - 4) * q^89 + (-b - 1) * q^91 + 7 * q^94 + (2*b - 10) * q^97 + (-3*b - 4) * q^98
$\operatorname{Tr}(f)(q)$	$=$	2 * q - 2 * q^2 + 2 * q^4 + 3 * q^7 - 2 * q^8 - 3 * q^11 - 2 * q^13 - 3 * q^14 + 2 * q^16 - 5 * q^17 + 3 * q^19 + 3 * q^22 + 2 * q^26 + 3 * q^28 - q^31 - 2 * q^32 + 5 * q^34 + 3 * q^37 - 3 * q^38 + q^41 - 10 * q^43 - 3 * q^44 - 14 * q^47 + 11 * q^49 - 2 * q^52 + 8 * q^53 - 3 * q^56 + q^59 + 9 * q^61 + q^62 + 2 * q^64 - 5 * q^68 - 3 * q^71 - 24 * q^73 - 3 * q^74 + 3 * q^76 - 25 * q^77 - 5 * q^79 - q^82 + 15 * q^83 + 10 * q^86 + 3 * q^88 - 10 * q^89 - 3 * q^91 + 14 * q^94 - 18 * q^97 - 11 * q^98

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

−2.70156
3.70156

−1.00000

0

1.00000

0

0

−1.70156

−1.00000

0

0

1.2

−1.00000

0

1.00000

0

0

4.70156

−1.00000

0

0

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$3$	$-1$
$5$	$-1$
$13$	$+1$

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	5850.2.a.cg		2
3.b	odd	2	1		1950.2.a.bg	yes	2
5.b	even	2	1		5850.2.a.cj		2
5.c	odd	4	2		5850.2.e.bi		4
15.d	odd	2	1		1950.2.a.bc	✓	2
15.e	even	4	2		1950.2.e.p		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1950.2.a.bc	✓	2	15.d	odd	2	1
1950.2.a.bg	yes	2	3.b	odd	2	1
1950.2.e.p		4	15.e	even	4	2
5850.2.a.cg		2	1.a	even	1	1	trivial
5850.2.a.cj		2	5.b	even	2	1
5850.2.e.bi		4	5.c	odd	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(5850))$:

$T_{7}^{2} - 3T_{7} - 8$

$T_{11}^{2} + 3T_{11} - 8$

$T_{17}^{2} + 5T_{17} - 4$

$T_{23}$

$T_{31}^{2} + T_{31} - 92$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$(T + 1)^{2}$
$3$	$T^{2}$
$5$	$T^{2}$
$7$	$T^{2} - 3T - 8$
$11$	$T^{2} + 3T - 8$