Properties

Label 983.2.a.b
Level $983$
Weight $2$
Character orbit 983.a
Self dual yes
Analytic conductor $7.849$
Analytic rank $0$
Dimension $54$
CM no
Inner twists $1$

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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: \(0\)
Dimension: \(54\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −2.79902 −1.37741 5.83449 −1.52700 3.85540 4.50391 −10.7328 −1.10273 4.27409
1.2 −2.59593 −0.548664 4.73883 3.85051 1.42429 −1.35607 −7.10979 −2.69897 −9.99563
1.3 −2.56280 2.68242 4.56793 0.599683 −6.87450 3.67314 −6.58109 4.19537 −1.53687
1.4 −2.55366 2.02223 4.52118 −4.30555 −5.16409 1.54441 −6.43825 1.08942 10.9949
1.5 −2.42129 0.803744 3.86265 3.28925 −1.94610 3.29937 −4.51003 −2.35400 −7.96423
1.6 −2.36689 −1.50082 3.60219 −1.85949 3.55227 0.0863179 −3.79222 −0.747553 4.40121
1.7 −2.28382 1.07395 3.21585 −3.29381 −2.45272 −2.40396 −2.77679 −1.84662 7.52248
1.8 −2.11673 −3.41526 2.48055 −2.85207 7.22918 3.49572 −1.01719 8.66400 6.03706
1.9 −2.08433 3.17224 2.34444 0.336118 −6.61201 −1.75412 −0.717929 7.06313 −0.700583
1.10 −1.83512 −2.37856 1.36768 −0.131265 4.36496 −4.16934 1.16038 2.65756 0.240888
1.11 −1.70929 −2.85036 0.921666 3.70678 4.87208 −1.37276 1.84318 5.12455 −6.33595
1.12 −1.58618 −1.33638 0.515976 0.931296 2.11975 2.81580 2.35393 −1.21408 −1.47721
1.13 −1.55013 −0.251970 0.402914 −1.29975 0.390586 −4.11447 2.47570 −2.93651 2.01479
1.14 −1.53339 2.66681 0.351281 4.12109 −4.08926 2.92035 2.52813 4.11188 −6.31924
1.15 −1.45073 1.34954 0.104610 3.00144 −1.95782 −1.88776 2.74969 −1.17873 −4.35427
1.16 −1.39657 1.31114 −0.0496049 −1.59833 −1.83110 4.09968 2.86241 −1.28090 2.23217
1.17 −1.13542 −1.73773 −0.710827 −4.00726 1.97305 3.34589 3.07792 0.0197210 4.54991
1.18 −1.00569 −0.156806 −0.988591 0.630600 0.157698 −3.47391 3.00559 −2.97541 −0.634187
1.19 −0.870233 −2.53615 −1.24269 1.03445 2.20704 5.14837 2.82190 3.43208 −0.900213
1.20 −0.773901 2.93267 −1.40108 2.13834 −2.26960 2.57212 2.63210 5.60055 −1.65486
See all 54 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.54
Significant digits:
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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.b 54
3.b odd 2 1 8847.2.a.g 54
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
983.2.a.b 54 1.a even 1 1 trivial
8847.2.a.g 54 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{54} - 8 T_{2}^{53} - 54 T_{2}^{52} + 584 T_{2}^{51} + 1042 T_{2}^{50} - 19796 T_{2}^{49} - 1237 T_{2}^{48} + 413466 T_{2}^{47} - 358794 T_{2}^{46} - 5952129 T_{2}^{45} + 8958894 T_{2}^{44} + 62553726 T_{2}^{43} + \cdots - 983 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(983))\). Copy content Toggle raw display