Newform orbit 16245.2.a.ct

• Label: 16245.2.a.ct
• Level: $16245$
• Weight: $2$
• Character orbit: 16245.a
• Self dual: yes
• Analytic conductor: $129.717$
• Dimension: $12$

Newspace parameters

Level:	$N$	$=$	$16245 = 3^{2} \cdot 5 \cdot 19^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	16245.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$129.716978084$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
Defining polynomial:	x^12 - 19*x^10 - 4*x^9 + 116*x^8 + 32*x^7 - 293*x^6 - 92*x^5 + 309*x^4 + 100*x^3 - 114*x^2 - 36*x + 1
Twist minimal:	not computed
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

The algebraic $q$-expansion of this newform has not been computed, but we have computed the trace expansion.

$\operatorname{Tr}(f)(q) =$ 12 * q - 4 * q^2 + 18 * q^4 + 12 * q^5 - 10 * q^7 - 18 * q^8 - 4 * q^10 - 22 * q^11 + 16 * q^13 - 4 * q^14 + 18 * q^16 - 8 * q^17 + 18 * q^20 + 14 * q^22 - 18 * q^23 + 12 * q^25 - 10 * q^26 - 20 * q^28 + 4 * q^29 + 20 * q^31 - 30 * q^32 - 10 * q^35 + 10 * q^37 - 18 * q^40 - 12 * q^41 - 22 * q^43 - 38 * q^44 + 20 * q^46 - 10 * q^47 - 4 * q^49 - 4 * q^50 + 54 * q^52 - 16 * q^53 - 22 * q^55 + 62 * q^56 - 4 * q^58 - 10 * q^59 + 12 * q^61 - 38 * q^62 + 24 * q^64 + 16 * q^65 + 36 * q^67 - 62 * q^68 - 4 * q^70 - 10 * q^71 - 48 * q^74 + 24 * q^77 - 4 * q^79 + 18 * q^80 - 42 * q^82 - 26 * q^83 - 8 * q^85 + 30 * q^86 + 78 * q^88 - 34 * q^89 - 28 * q^91 - 12 * q^92 + 16 * q^94 + 50 * q^97 - 20 * q^98

Atkin-Lehner signs

$p$	Sign
$3$	$-1$
$5$	$-1$
$19$	$+1$

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.