Newform orbit 45570.2.a.cx

• Label: 45570.2.a.cx
• Level: $45570$
• Weight: $2$
• Character orbit: 45570.a
• Self dual: yes
• Analytic conductor: $363.878$
• Dimension: $1$

Newspace parameters

Level:	$N$	$=$	$45570 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 31$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	45570.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$363.878282011$
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^5 + q^6 + q^8 + q^9 - q^10 + q^12 + 6 * q^13 - q^15 + q^16 - 2 * q^17 + q^18 + 4 * q^19 - q^20 - 4 * q^23 + q^24 + q^25 + 6 * q^26 + q^27 + 4 * q^29 - q^30 - q^31 + q^32 - 2 * q^34 + q^36 + 2 * q^37 + 4 * q^38 + 6 * q^39 - q^40 - 6 * q^41 - 2 * q^43 - q^45 - 4 * q^46 - 2 * q^47 + q^48 + q^50 - 2 * q^51 + 6 * q^52 + q^54 + 4 * q^57 + 4 * q^58 - 6 * q^59 - q^60 + 10 * q^61 - q^62 + q^64 - 6 * q^65 - 2 * q^68 - 4 * q^69 + 8 * q^71 + q^72 + 2 * q^73 + 2 * q^74 + q^75 + 4 * q^76 + 6 * q^78 + 10 * q^79 - q^80 + q^81 - 6 * q^82 + 4 * q^83 + 2 * q^85 - 2 * q^86 + 4 * q^87 + 10 * q^89 - q^90 - 4 * q^92 - q^93 - 2 * q^94 - 4 * q^95 + q^96 + 12 * q^97

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$-1$
$5$	$+1$
$7$	$-1$
$31$	$+1$

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.