Newform orbit 28749.2.a.a

• Label: 28749.2.a.a
• Level: $28749$
• Weight: $2$
• Character orbit: 28749.a
• Self dual: yes
• Analytic conductor: $229.562$
• Dimension: $1$

Newspace parameters

Level:	$N$	$=$	$28749 = 3 \cdot 7 \cdot 37^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	28749.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$229.561920771$
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 + 2 * q^5 + q^6 - q^7 + 3 * q^8 + q^9 - 2 * q^10 + 4 * q^11 + q^12 - 2 * q^13 + q^14 - 2 * q^15 - q^16 - 2 * q^17 - q^18 - 4 * q^19 - 2 * q^20 + q^21 - 4 * q^22 - 3 * q^24 - q^25 + 2 * q^26 - q^27 + q^28 - 10 * q^29 + 2 * q^30 - 5 * q^32 - 4 * q^33 + 2 * q^34 - 2 * q^35 - q^36 + 4 * q^38 + 2 * q^39 + 6 * q^40 - 6 * q^41 - q^42 - 8 * q^43 - 4 * q^44 + 2 * q^45 + q^48 + q^49 + q^50 + 2 * q^51 + 2 * q^52 + 14 * q^53 + q^54 + 8 * q^55 - 3 * q^56 + 4 * q^57 + 10 * q^58 + 8 * q^59 + 2 * q^60 + 14 * q^61 - q^63 + 7 * q^64 - 4 * q^65 + 4 * q^66 - 12 * q^67 + 2 * q^68 + 2 * q^70 + 8 * q^71 + 3 * q^72 + 10 * q^73 + q^75 + 4 * q^76 - 4 * q^77 - 2 * q^78 - 4 * q^79 - 2 * q^80 + q^81 + 6 * q^82 + 12 * q^83 - q^84 - 4 * q^85 + 8 * q^86 + 10 * q^87 + 12 * q^88 + 14 * q^89 - 2 * q^90 + 2 * q^91 - 8 * q^95 + 5 * q^96 - 6 * q^97 - q^98 + 4 * q^99

Atkin-Lehner signs

$p$	Sign
$3$	$+1$
$7$	$+1$
$37$	$+1$

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.