Newform orbit 47850.2.a.bz

• Label: 47850.2.a.bz
• Level: $47850$
• Weight: $2$
• Character orbit: 47850.a
• Self dual: yes
• Analytic conductor: $382.084$
• Dimension: $1$

Newspace parameters

Level:	$N$	$=$	$47850 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	47850.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$382.084173672$
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^3 + q^4 - q^6 + q^8 + q^9 + q^11 - q^12 + 2 * q^13 + q^16 - 6 * q^17 + q^18 - 4 * q^19 + q^22 + 8 * q^23 - q^24 + 2 * q^26 - q^27 + q^29 + q^32 - q^33 - 6 * q^34 + q^36 - 10 * q^37 - 4 * q^38 - 2 * q^39 - 6 * q^41 + 12 * q^43 + q^44 + 8 * q^46 + 8 * q^47 - q^48 - 7 * q^49 + 6 * q^51 + 2 * q^52 + 10 * q^53 - q^54 + 4 * q^57 + q^58 - 8 * q^59 + 2 * q^61 + q^64 - q^66 - 6 * q^68 - 8 * q^69 + 12 * q^71 + q^72 - 10 * q^73 - 10 * q^74 - 4 * q^76 - 2 * q^78 - 8 * q^79 + q^81 - 6 * q^82 + 12 * q^86 - q^87 + q^88 - 10 * q^89 + 8 * q^92 + 8 * q^94 - q^96 + 10 * q^97 - 7 * q^98 + q^99

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$+1$
$5$	$+1$
$11$	$-1$
$29$	$-1$

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.