Properties

Label 983.4.a.b
Level $983$
Weight $4$
Character orbit 983.a
Self dual yes
Analytic conductor $57.999$
Analytic rank $0$
Dimension $136$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 983 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 983.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(57.9988775356\)
Analytic rank: \(0\)
Dimension: \(136\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9} + 257 q^{10} + 204 q^{11} + 296 q^{12} + 530 q^{13} + 103 q^{14} + 226 q^{15} + 2737 q^{16} + 664 q^{17} + 949 q^{18} + 421 q^{19} + 500 q^{20} + 684 q^{21} + 905 q^{22} + 617 q^{23} + 917 q^{24} + 5430 q^{25} + 572 q^{26} + 886 q^{27} + 2728 q^{28} + 688 q^{29} + 712 q^{30} + 1019 q^{31} + 2363 q^{32} + 1764 q^{33} + 1260 q^{34} + 834 q^{35} + 7190 q^{36} + 3303 q^{37} + 384 q^{38} + 1950 q^{39} + 2766 q^{40} + 1975 q^{41} + 448 q^{42} + 3021 q^{43} + 2038 q^{44} + 2266 q^{45} + 2742 q^{46} + 1293 q^{47} + 2589 q^{48} + 10447 q^{49} + 2191 q^{50} + 1032 q^{51} + 4983 q^{52} + 2415 q^{53} + 1878 q^{54} + 2612 q^{55} + 1540 q^{56} + 7908 q^{57} + 5743 q^{58} + 1059 q^{59} + 2611 q^{60} + 4312 q^{61} + 3258 q^{62} + 5605 q^{63} + 13735 q^{64} + 3554 q^{65} + 433 q^{66} + 5715 q^{67} + 5881 q^{68} + 1398 q^{69} + 4287 q^{70} + 2530 q^{71} + 9891 q^{72} + 14106 q^{73} + 2318 q^{74} + 2621 q^{75} + 4651 q^{76} + 4750 q^{77} + 6639 q^{78} + 4791 q^{79} + 4812 q^{80} + 19932 q^{81} + 5380 q^{82} + 4284 q^{83} + 9282 q^{84} + 12058 q^{85} + 2451 q^{86} + 6984 q^{87} + 11197 q^{88} + 5313 q^{89} + 5405 q^{90} + 6298 q^{91} + 6588 q^{92} + 5700 q^{93} + 4743 q^{94} + 5778 q^{95} + 9613 q^{96} + 15382 q^{97} + 6640 q^{98} + 8542 q^{99}+O(q^{100}) \) 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 −5.48302 6.58697 22.0635 1.06908 −36.1165 −11.0216 −77.1106 16.3882 −5.86179
1.2 −5.46364 9.02325 21.8513 10.0186 −49.2998 33.9408 −75.6787 54.4191 −54.7380
1.3 −5.42093 −6.60411 21.3865 −7.49992 35.8004 7.21303 −72.5672 16.6143 40.6566
1.4 −5.41843 −4.91964 21.3594 −14.8199 26.6567 −18.4130 −72.3871 −2.79713 80.3006
1.5 −5.35973 4.00201 20.7267 −16.3566 −21.4497 27.2191 −68.2115 −10.9839 87.6670
1.6 −5.25160 3.19215 19.5793 −16.3542 −16.7639 −21.7601 −60.8100 −16.8102 85.8857
1.7 −5.21995 1.22531 19.2479 −7.13968 −6.39604 24.4412 −58.7133 −25.4986 37.2688
1.8 −5.14175 −9.46258 18.4375 15.7096 48.6542 4.70054 −53.6672 62.5405 −80.7748
1.9 −5.10403 2.85786 18.0511 7.24893 −14.5866 −25.2920 −51.3012 −18.8326 −36.9987
1.10 −5.09377 −7.01437 17.9465 9.92667 35.7296 28.3391 −50.6651 22.2014 −50.5642
1.11 −5.07699 −3.00401 17.7758 4.72008 15.2513 18.0052 −49.6315 −17.9759 −23.9638
1.12 −4.82266 −8.16418 15.2580 −21.8591 39.3730 14.7056 −35.0029 39.6538 105.419
1.13 −4.81837 2.07447 15.2167 4.44379 −9.99556 −32.3361 −34.7726 −22.6966 −21.4118
1.14 −4.73019 8.15103 14.3747 17.4955 −38.5560 −16.0796 −30.1537 39.4393 −82.7572
1.15 −4.51197 −7.25700 12.3578 17.5119 32.7433 −15.6407 −19.6624 25.6640 −79.0132
1.16 −4.48719 −1.56623 12.1348 −16.6701 7.02795 18.2427 −18.5538 −24.5469 74.8017
1.17 −4.42652 0.575567 11.5941 8.51872 −2.54776 −6.14380 −15.9092 −26.6687 −37.7083
1.18 −4.27714 9.48940 10.2939 −14.7336 −40.5875 26.9751 −9.81140 63.0488 63.0176
1.19 −4.26495 3.59666 10.1898 20.6855 −15.3396 34.9677 −9.33931 −14.0641 −88.2228
1.20 −4.19855 −6.41050 9.62784 2.10538 26.9148 −18.0497 −6.83459 14.0945 −8.83954
See next 80 embeddings (of 136 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.136
Significant digits:
Format:

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 983.4.a.b 136
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
983.4.a.b 136 1.a even 1 1 trivial