Properties

Label 983.6.a.b
Level $983$
Weight $6$
Character orbit 983.a
Self dual yes
Analytic conductor $157.657$
Analytic rank $0$
Dimension $218$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 983 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 983.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(157.657294876\)
Analytic rank: \(0\)
Dimension: \(218\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9} + 2133 q^{10} + 1752 q^{11} + 3512 q^{12} + 5990 q^{13} + 2319 q^{14} + 4639 q^{15} + 66105 q^{16} + 10656 q^{17} + 11911 q^{18} + 11511 q^{19} + 10012 q^{20} + 12225 q^{21} + 19401 q^{22} + 9767 q^{23} + 21725 q^{24} + 185207 q^{25} + 7708 q^{26} + 23764 q^{27} + 77808 q^{28} + 25772 q^{29} + 15736 q^{30} + 35900 q^{31} + 60155 q^{32} + 70026 q^{33} + 17236 q^{34} + 28782 q^{35} + 382874 q^{36} + 126082 q^{37} + 62164 q^{38} + 54264 q^{39} + 102846 q^{40} + 70480 q^{41} + 102244 q^{42} + 137413 q^{43} + 116278 q^{44} + 93481 q^{45} + 126122 q^{46} + 63218 q^{47} + 124701 q^{48} + 732031 q^{49} + 131089 q^{50} + 109902 q^{51} + 229519 q^{52} + 102608 q^{53} + 149130 q^{54} + 167596 q^{55} + 87868 q^{56} + 408318 q^{57} + 304579 q^{58} + 67460 q^{59} + 150523 q^{60} + 195132 q^{61} + 132294 q^{62} + 374425 q^{63} + 1296639 q^{64} + 347092 q^{65} + 147397 q^{66} + 381238 q^{67} + 296321 q^{68} + 139362 q^{69} + 325675 q^{70} + 147818 q^{71} + 646059 q^{72} + 961992 q^{73} + 167410 q^{74} + 167324 q^{75} + 504875 q^{76} + 284328 q^{77} + 284295 q^{78} + 285792 q^{79} + 444932 q^{80} + 1980282 q^{81} + 336676 q^{82} + 276734 q^{83} + 378474 q^{84} + 1021245 q^{85} + 156051 q^{86} + 500457 q^{87} + 1068101 q^{88} + 398983 q^{89} + 463961 q^{90} + 273517 q^{91} + 577884 q^{92} + 967833 q^{93} + 224775 q^{94} + 482817 q^{95} + 780445 q^{96} + 1636277 q^{97} + 495958 q^{98} + 627643 q^{99}+O(q^{100}) \) 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 −11.2545 14.3637 94.6632 5.42124 −161.655 48.2201 −705.242 −36.6855 −61.0132
1.2 −11.0647 −25.4268 90.4285 75.4706 281.341 155.090 −646.496 403.521 −835.063
1.3 −11.0396 −16.6850 89.8732 −54.0018 184.196 −10.8436 −638.898 35.3900 596.159
1.4 −11.0108 −2.28470 89.2387 53.2861 25.1565 −155.822 −630.246 −237.780 −586.724
1.5 −11.0085 27.1723 89.1872 −88.2795 −299.126 52.5145 −629.545 495.333 971.825
1.6 −10.8442 −6.29114 85.5966 9.46707 68.2223 −20.0151 −581.212 −203.422 −102.663
1.7 −10.7977 −15.2978 84.5913 −106.934 165.182 232.255 −567.867 −8.97689 1154.65
1.8 −10.7909 23.9514 84.4434 90.3849 −258.457 150.379 −565.911 330.669 −975.334
1.9 −10.6923 3.77147 82.3260 −15.6343 −40.3258 194.820 −538.102 −228.776 167.167
1.10 −10.6888 −2.78158 82.2511 63.0885 29.7318 −133.230 −537.126 −235.263 −674.342
1.11 −10.4420 0.0889574 77.0361 −100.525 −0.928896 31.6163 −470.268 −242.992 1049.69
1.12 −10.3513 9.89991 75.1501 97.3083 −102.477 −91.6942 −446.662 −144.992 −1007.27
1.13 −10.1039 11.1728 70.0889 83.9898 −112.889 92.1063 −384.847 −118.168 −848.625
1.14 −10.0849 8.47019 69.7046 6.04415 −85.4208 −170.780 −380.247 −171.256 −60.9545
1.15 −10.0174 −24.0669 68.3476 39.3861 241.087 −242.470 −364.107 336.214 −394.545
1.16 −9.86337 −14.1514 65.2861 8.97631 139.581 −99.2905 −328.313 −42.7375 −88.5367
1.17 −9.77516 −29.0216 63.5537 −38.6585 283.690 235.286 −308.442 599.250 377.893
1.18 −9.74643 22.6936 62.9930 3.05529 −221.181 −41.0311 −302.071 271.998 −29.7782
1.19 −9.67677 −17.9132 61.6399 −79.1572 173.342 −217.764 −286.818 77.8823 765.986
1.20 −9.61332 27.9669 60.4159 −41.3834 −268.854 221.300 −273.171 539.145 397.832
See next 80 embeddings (of 218 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.218
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 983.6.a.b 218
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
983.6.a.b 218 1.a even 1 1 trivial