Properties

Label 983.4.a.a
Level $983$
Weight $4$
Character orbit 983.a
Self dual yes
Analytic conductor $57.999$
Analytic rank $1$
Dimension $109$
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: \(1\)
Dimension: \(109\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9} - 243 q^{10} - 126 q^{11} - 280 q^{12} - 458 q^{13} - 177 q^{14} - 314 q^{15} + 1009 q^{16} - 594 q^{17} - 671 q^{18} - 491 q^{19} - 500 q^{20} - 660 q^{21} - 899 q^{22} - 487 q^{23} - 811 q^{24} + 705 q^{25} - 104 q^{26} - 842 q^{27} - 2648 q^{28} - 820 q^{29} - 728 q^{30} - 965 q^{31} - 1669 q^{32} - 2196 q^{33} - 508 q^{34} - 846 q^{35} + 1358 q^{36} - 3209 q^{37} - 1136 q^{38} - 1326 q^{39} - 3234 q^{40} - 1961 q^{41} - 2240 q^{42} - 2999 q^{43} - 1922 q^{44} - 2234 q^{45} - 2962 q^{46} - 1903 q^{47} - 2787 q^{48} + 1186 q^{49} - 2309 q^{50} - 2436 q^{51} - 4897 q^{52} - 1825 q^{53} - 3306 q^{54} - 2888 q^{55} - 1820 q^{56} - 6684 q^{57} - 4813 q^{58} - 1537 q^{59} - 3869 q^{60} - 2276 q^{61} - 1950 q^{62} - 6491 q^{63} - 89 q^{64} - 5546 q^{65} - 3527 q^{66} - 5005 q^{67} - 4183 q^{68} - 3018 q^{69} - 2993 q^{70} - 2014 q^{71} - 9549 q^{72} - 12904 q^{73} - 2714 q^{74} - 3379 q^{75} - 6293 q^{76} - 3258 q^{77} - 4593 q^{78} - 5005 q^{79} - 3988 q^{80} + 249 q^{81} - 5116 q^{82} - 2854 q^{83} - 4158 q^{84} - 11742 q^{85} - 2709 q^{86} - 2412 q^{87} - 10451 q^{88} - 2519 q^{89} - 8095 q^{90} - 2438 q^{91} - 6660 q^{92} - 10668 q^{93} - 4281 q^{94} - 4482 q^{95} - 6515 q^{96} - 16628 q^{97} - 5708 q^{98} - 6308 q^{99}+O(q^{100}) \) 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 −5.58646 −0.724275 23.2085 15.1603 4.04613 11.0308 −84.9620 −26.4754 −84.6926
1.2 −5.43981 −4.19474 21.5915 −1.69960 22.8186 −29.9614 −73.9355 −9.40415 9.24553
1.3 −5.36058 −0.495047 20.7358 −12.0516 2.65374 −0.578955 −68.2712 −26.7549 64.6036
1.4 −5.35691 −6.65704 20.6965 16.4748 35.6612 −32.9904 −68.0141 17.3161 −88.2542
1.5 −5.26153 −9.03263 19.6837 −5.00636 47.5254 5.47420 −61.4739 54.5884 26.3411
1.6 −5.25670 8.92364 19.6329 −14.6619 −46.9089 −4.44244 −61.1508 52.6313 77.0735
1.7 −5.11709 4.98154 18.1846 19.4669 −25.4910 −11.1023 −52.1157 −2.18425 −99.6141
1.8 −4.98778 3.08939 16.8780 10.2056 −15.4092 13.1728 −44.2815 −17.4557 −50.9035
1.9 −4.84438 −3.38875 15.4680 9.70346 16.4164 −1.30349 −36.1777 −15.5163 −47.0072
1.10 −4.76983 4.01927 14.7512 −2.78342 −19.1712 17.1208 −32.2023 −10.8454 13.2764
1.11 −4.76719 8.84156 14.7261 −7.92466 −42.1494 −15.4085 −32.0645 51.1732 37.7783
1.12 −4.74560 9.89469 14.5207 10.6639 −46.9563 −4.53278 −30.9447 70.9049 −50.6066
1.13 −4.67338 5.53617 13.8405 −1.05395 −25.8727 16.9979 −27.2950 3.64920 4.92552
1.14 −4.63586 −1.39484 13.4912 −1.90865 6.46628 −14.9064 −25.4564 −25.0544 8.84822
1.15 −4.54428 −2.38245 12.6505 −17.0184 10.8265 −0.746020 −21.1331 −21.3239 77.3363
1.16 −4.46204 −5.70729 11.9098 −10.3218 25.4662 32.8198 −17.4456 5.57321 46.0562
1.17 −4.42678 −9.72553 11.5964 −7.04425 43.0527 −25.6819 −15.9203 67.5859 31.1833
1.18 −4.32365 6.42278 10.6939 0.242187 −27.7698 13.8062 −11.6476 14.2521 −1.04713
1.19 −4.23489 5.14870 9.93428 −19.0899 −21.8042 −26.8153 −8.19147 −0.490926 80.8438
1.20 −4.06969 −3.69076 8.56235 −18.1705 15.0202 −23.3834 −2.28858 −13.3783 73.9482
See next 80 embeddings (of 109 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.109
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.a 109
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
983.4.a.a 109 1.a even 1 1 trivial