Newform orbit 983.2.a.a

• Label: 983.2.a.a
• Level: $983$
• Weight: $2$
• Character orbit: 983.a
• Self dual: yes
• Analytic conductor: $7.849$
• Analytic rank: $1$
• Dimension: $28$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(7.84929451869\)
Analytic rank:	\(1\)
Dimension:	\(28\)
Twist minimal:	yes
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1.1	−2.75257			2.22028			5.57661			0.543842			−6.11147			−3.48299			−9.84486			1.92965			−1.49696
1.2	−2.57328			−2.39055			4.62176			1.19059			6.15156			−1.20078			−6.74651			2.71475			−3.06371
1.3	−2.42034			−0.187530			3.85806			−0.842553			0.453886			−4.42798			−4.49714			−2.96483			2.03927
1.4	−2.21759			0.931642			2.91773			0.396530			−2.06600			2.27074			−2.03515			−2.13204			−0.879344
1.5	−2.05764			−2.81984			2.23388			0.650217			5.80222			0.324376			−0.481237			4.95151			−1.33791
1.6	−1.91443			1.82487			1.66503			2.84047			−3.49358			−3.81993			0.641279			0.330154			−5.43787
1.7	−1.85163			−0.818723			1.42855			−3.13539			1.51597			0.698052			1.05812			−2.32969			5.80559
1.8	−1.64859			2.69101			0.717863			−2.78854			−4.43639			−0.853736			2.11372			4.24155			4.59718
1.9	−1.64741			−0.803598			0.713964			2.48769			1.32386			2.09423			2.11863			−2.35423			−4.09824
1.10	−0.971766			−2.84689			−1.05567			−2.58229			2.76651			−3.41775			2.96940			5.10478			2.50939
1.11	−0.930689			−1.12871			−1.13382			3.65614			1.05048			−1.39504			2.91661			−1.72601			−3.40273
1.12	−0.875382			0.413140			−1.23371			0.141089			−0.361655			−0.646767			2.83073			−2.82932			−0.123507
1.13	−0.468024			−2.30825			−1.78095			−2.20940			1.08031			0.238349			1.76958			2.32800			1.03405
1.14	−0.434502			1.46359			−1.81121			−1.89683			−0.635931			1.45633			1.65598			−0.857914			0.824176
1.15	−0.400086			2.91622			−1.83993			0.291591			−1.16674			−3.58224			1.53630			5.50433			−0.116661
1.16	−0.120414			−1.94834			−1.98550			0.840169			0.234608			−0.0546560			0.479911			0.796025			−0.101168
1.17	0.0562061			0.611738			−1.99684			0.503583			0.0343834			3.25094			−0.224647			−2.62578			0.0283044
1.18	0.413754			0.397482			−1.82881			1.10128			0.164460			−2.64498			−1.58419			−2.84201			0.455658
1.19	0.768290			1.84565			−1.40973			−1.02856			1.41799			−1.07434			−2.61966			0.406425			−0.790236
1.20	0.912923			−2.89686			−1.16657			−1.17872			−2.64461			3.45815			−2.89084			5.39181			−1.07608

Atkin-Lehner signs

\( p \)	Sign
\(983\)	\(1\)

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	983.2.a.a	✓	28
3.b	odd	2	1		8847.2.a.b		28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
983.2.a.a	✓	28	1.a	even	1	1	trivial
8847.2.a.b		28	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^28 + 7*T2^27 - 12*T2^26 - 184*T2^25 - 110*T2^24 + 2026*T2^23 + 3083*T2^22 - 12045*T2^21 - 26802*T2^20 + 40855*T2^19 + 128063*T2^18 - 71590*T2^17 - 378054*T2^16 + 15476*T2^15 + 712577*T2^14 + 202920*T2^13 - 849928*T2^12 - 443102*T2^11 + 608717*T2^10 + 448651*T2^9 - 226391*T2^8 - 238743*T2^7 + 21942*T2^6 + 60980*T2^5 + 8363*T2^4 - 5156*T2^3 - 1394*T2^2 - 32*T2 + 7