Newform orbit 37845.2.a.d

• Label: 37845.2.a.d
• Level: $37845$
• Weight: $2$
• Character orbit: 37845.a
• Self dual: yes
• Analytic conductor: $302.194$
• Dimension: $1$

Newspace parameters

Level:	$N$	$=$	$37845 = 3^{2} \cdot 5 \cdot 29^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	37845.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$302.193846450$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	not computed
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - q^2 - q^4 - q^5 + 3 * q^8 + q^10 - 4 * q^11 - 2 * q^13 - q^16 + 2 * q^17 - 4 * q^19 + q^20 + 4 * q^22 + q^25 + 2 * q^26 - 5 * q^32 - 2 * q^34 + 10 * q^37 + 4 * q^38 - 3 * q^40 + 10 * q^41 - 4 * q^43 + 4 * q^44 + 8 * q^47 - 7 * q^49 - q^50 + 2 * q^52 + 10 * q^53 + 4 * q^55 + 4 * q^59 + 2 * q^61 + 7 * q^64 + 2 * q^65 + 12 * q^67 - 2 * q^68 + 8 * q^71 - 10 * q^73 - 10 * q^74 + 4 * q^76 + q^80 - 10 * q^82 - 12 * q^83 - 2 * q^85 + 4 * q^86 - 12 * q^88 - 6 * q^89 - 8 * q^94 + 4 * q^95 - 2 * q^97 + 7 * q^98

Atkin-Lehner signs

$p$	Sign
$3$	$-1$
$5$	$+1$
$29$	$+1$

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.