Newform orbit 10004.2.a.b

• Label: 10004.2.a.b
• Level: $10004$
• Weight: $2$
• Character orbit: 10004.a
• Self dual: yes
• Analytic conductor: $79.882$
• Dimension: $42$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 10004 = 2^{2} \cdot 41 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	10004.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(79.8823421821\)
Dimension:	\(42\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) 42 * q - q^3 - 12 * q^5 - 8 * q^7 + 29 * q^9 - 3 * q^11 - 19 * q^13 - 3 * q^15 - 17 * q^17 + q^19 - 22 * q^21 - 2 * q^23 + 14 * q^25 + 8 * q^27 - 7 * q^29 - 32 * q^31 - 18 * q^33 + 12 * q^35 - 28 * q^37 - 12 * q^39 - 42 * q^41 - 18 * q^43 - 15 * q^45 - 17 * q^47 - 14 * q^49 - 6 * q^51 - q^53 - 21 * q^55 - 39 * q^57 - 25 * q^59 + 42 * q^61 - 27 * q^63 - 13 * q^65 - 5 * q^67 - 30 * q^69 - 4 * q^71 - 47 * q^73 - 6 * q^75 - 15 * q^77 - 24 * q^79 - 66 * q^81 + 5 * q^83 - 82 * q^85 - 14 * q^87 - 8 * q^89 - 14 * q^91 - 13 * q^93 - 9 * q^95 - 59 * q^97 - 33 * q^99

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( -1 \)
\(41\)	\( +1 \)
\(61\)	\( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

Twists of this newform have not been computed.