Newform orbit 16245.2.a.co

• Label: 16245.2.a.co
• Level: $16245$
• Weight: $2$
• Character orbit: 16245.a
• Self dual: yes
• Analytic conductor: $129.717$
• Dimension: $9$

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:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
Defining polynomial:	$x^{9} - 12x^{7} - 4x^{6} + 48x^{5} + 27x^{4} - 72x^{3} - 51x^{2} + 27x + 19$
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.

$\operatorname{Tr}(f)(q) =$ 9 * q + 6 * q^4 + 9 * q^5 - 12 * q^8 + 3 * q^13 + 12 * q^14 - 12 * q^16 + 9 * q^17 + 6 * q^20 - 12 * q^22 + 9 * q^25 - 21 * q^26 - 15 * q^28 + 15 * q^29 - 30 * q^31 - 9 * q^32 - 30 * q^37 - 12 * q^40 + 18 * q^41 - 6 * q^43 + 24 * q^44 - 21 * q^46 - 21 * q^47 + 3 * q^49 + 3 * q^52 - 9 * q^53 + 36 * q^56 + 18 * q^58 + 27 * q^59 + 12 * q^61 + 6 * q^62 + 24 * q^64 + 3 * q^65 - 36 * q^67 - 3 * q^68 + 12 * q^70 - 6 * q^71 - 9 * q^73 + 9 * q^74 - 12 * q^77 - 45 * q^79 - 12 * q^80 - 48 * q^82 + 9 * q^85 - 9 * q^86 - 39 * q^88 - 9 * q^89 - 51 * q^91 + 54 * q^92 - 33 * q^94 - 45 * q^97 + 33 * 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.