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Properties

Label 483.2.q.f
Level $483$
Weight $2$
Character orbit 483.q
Analytic conductor $3.857$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.q (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(8\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 80q + q^{2} - 8q^{3} - 9q^{4} + 13q^{5} + q^{6} + 8q^{7} - 25q^{8} - 8q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 80q + q^{2} - 8q^{3} - 9q^{4} + 13q^{5} + q^{6} + 8q^{7} - 25q^{8} - 8q^{9} + 4q^{10} + q^{11} - 9q^{12} - 26q^{13} - q^{14} + 2q^{15} - 3q^{16} - 23q^{17} + q^{18} + 10q^{19} + 63q^{20} + 8q^{21} - 9q^{23} + 30q^{24} - 29q^{25} - 12q^{26} - 8q^{27} + 20q^{28} + 13q^{29} + 4q^{30} - 27q^{31} + 71q^{32} + q^{33} - 45q^{34} - 2q^{35} - 9q^{36} + 60q^{37} - 2q^{38} - 26q^{39} + 7q^{40} - 26q^{41} - q^{42} + 5q^{43} - 33q^{44} - 20q^{45} - 41q^{46} + 34q^{47} - 58q^{48} - 8q^{49} - 75q^{50} - q^{51} + 108q^{52} - 39q^{53} - 10q^{54} + 51q^{55} + 3q^{56} + 10q^{57} + 47q^{58} - 66q^{59} + 19q^{60} + 3q^{61} + 103q^{62} + 8q^{63} - 25q^{64} + 39q^{65} - 33q^{66} + 33q^{67} - 88q^{68} + 13q^{69} + 18q^{70} - 12q^{71} - 25q^{72} - 98q^{73} + 123q^{74} + 4q^{75} - 41q^{76} - 12q^{77} + 10q^{78} - 34q^{79} + 163q^{80} - 8q^{81} + 48q^{82} + 26q^{83} + 9q^{84} + 35q^{85} + 4q^{86} + 2q^{87} + 178q^{88} - 63q^{89} + 4q^{90} - 62q^{91} - 39q^{92} + 138q^{93} - 28q^{94} - 80q^{95} - 17q^{96} - 44q^{97} + q^{98} + q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
64.1 −2.58285 − 0.758394i −0.654861 + 0.755750i 4.41347 + 2.83636i 0.585697 − 4.07361i 2.26457 − 1.45535i −0.415415 − 0.909632i −5.72263 − 6.60426i −0.142315 − 0.989821i −4.60218 + 10.0774i
64.2 −2.29822 − 0.674819i −0.654861 + 0.755750i 3.14394 + 2.02049i −0.337260 + 2.34570i 2.01501 − 1.29497i −0.415415 − 0.909632i −2.72491 − 3.14472i −0.142315 − 0.989821i 2.35802 − 5.16334i
64.3 −1.60503 − 0.471280i −0.654861 + 0.755750i 0.671521 + 0.431561i 0.344040 − 2.39285i 1.40724 − 0.904381i −0.415415 − 0.909632i 1.31647 + 1.51928i −0.142315 − 0.989821i −1.67990 + 3.67846i
64.4 −0.545660 − 0.160220i −0.654861 + 0.755750i −1.41043 − 0.906430i −0.339288 + 2.35980i 0.478418 − 0.307461i −0.415415 − 0.909632i 1.36922 + 1.58017i −0.142315 − 0.989821i 0.563223 − 1.23329i
64.5 −0.326470 − 0.0958603i −0.654861 + 0.755750i −1.58511 − 1.01869i −0.00655525 + 0.0455927i 0.286239 − 0.183955i −0.415415 − 0.909632i 0.865477 + 0.998813i −0.142315 − 0.989821i 0.00651063 − 0.0142563i
64.6 1.23378 + 0.362270i −0.654861 + 0.755750i −0.291534 − 0.187358i 0.256312 − 1.78269i −1.08174 + 0.695192i −0.415415 − 0.909632i −1.97594 − 2.28036i −0.142315 − 0.989821i 0.962047 − 2.10659i
64.7 1.23794 + 0.363493i −0.654861 + 0.755750i −0.282132 − 0.181316i −0.594222 + 4.13291i −1.08539 + 0.697537i −0.415415 − 0.909632i −1.97317 − 2.27715i −0.142315 − 0.989821i −2.23789 + 4.90030i
64.8 2.67036 + 0.784088i −0.654861 + 0.755750i 4.83351 + 3.10631i 0.534653 − 3.71859i −2.34129 + 1.50465i −0.415415 − 0.909632i 6.82652 + 7.87822i −0.142315 − 0.989821i 4.34342 − 9.51076i
85.1 −1.83093 + 2.11301i 0.841254 − 0.540641i −0.827862 − 5.75791i 0.00406880 + 0.00890943i −0.397900 + 2.76745i 0.959493 − 0.281733i 8.97813 + 5.76989i 0.415415 − 0.909632i −0.0262754 − 0.00771515i
85.2 −1.24645 + 1.43848i 0.841254 − 0.540641i −0.230954 − 1.60632i 0.274912 + 0.601974i −0.270879 + 1.88400i 0.959493 − 0.281733i −0.603914 − 0.388112i 0.415415 − 0.909632i −1.20859 − 0.354874i
85.3 −0.723306 + 0.834739i 0.841254 − 0.540641i 0.111011 + 0.772099i −1.01603 − 2.22480i −0.157189 + 1.09328i 0.959493 − 0.281733i −2.58316 − 1.66009i 0.415415 − 0.909632i 2.59204 + 0.761090i
85.4 0.0321112 − 0.0370583i 0.841254 − 0.540641i 0.284287 + 1.97726i 1.63623 + 3.58284i 0.00697843 − 0.0485360i 0.959493 − 0.281733i 0.164905 + 0.105978i 0.415415 − 0.909632i 0.185315 + 0.0544134i
85.5 0.150977 − 0.174237i 0.841254 − 0.540641i 0.277065 + 1.92703i −0.602841 − 1.32004i 0.0328104 − 0.228201i 0.959493 − 0.281733i 0.765488 + 0.491950i 0.415415 − 0.909632i −0.321014 − 0.0942582i
85.6 1.00586 − 1.16083i 0.841254 − 0.540641i −0.0511307 − 0.355622i −0.0685636 − 0.150133i 0.218595 − 1.52036i 0.959493 − 0.281733i 2.12008 + 1.36249i 0.415415 − 0.909632i −0.243244 − 0.0714230i
85.7 1.32935 − 1.53415i 0.841254 − 0.540641i −0.301820 − 2.09921i −1.44923 − 3.17337i 0.288895 − 2.00931i 0.959493 − 0.281733i −0.206281 − 0.132568i 0.415415 − 0.909632i −6.79496 − 1.99518i
85.8 1.72933 − 1.99575i 0.841254 − 0.540641i −0.707820 − 4.92300i 1.53294 + 3.35668i 0.375820 − 2.61388i 0.959493 − 0.281733i −6.60605 − 4.24545i 0.415415 − 0.909632i 9.35007 + 2.74543i
127.1 −2.21932 + 1.42627i −0.142315 + 0.989821i 2.06030 − 4.51143i −2.63138 + 0.772642i −1.09591 − 2.39971i 0.654861 + 0.755750i 1.11117 + 7.72832i −0.959493 − 0.281733i 4.73787 − 5.46779i
127.2 −1.76396 + 1.13363i −0.142315 + 0.989821i 0.995613 − 2.18009i 3.41611 − 1.00306i −0.871052 − 1.90734i 0.654861 + 0.755750i 0.118370 + 0.823281i −0.959493 − 0.281733i −4.88878 + 5.64196i
127.3 −1.32987 + 0.854653i −0.142315 + 0.989821i 0.207281 − 0.453882i 0.177622 − 0.0521546i −0.656694 − 1.43796i 0.654861 + 0.755750i −0.337691 − 2.34869i −0.959493 − 0.281733i −0.191640 + 0.221164i
127.4 0.346757 − 0.222847i −0.142315 + 0.989821i −0.760251 + 1.66472i 2.21096 − 0.649197i 0.171230 + 0.374942i 0.654861 + 0.755750i 0.224677 + 1.56266i −0.959493 − 0.281733i 0.621994 − 0.717820i
See all 80 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 463.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.c even 11 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 483.2.q.f ✓ 80
23.c even 11 1 inner 483.2.q.f ✓ 80
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.2.q.f ✓ 80 1.a even 1 1 trivial
483.2.q.f ✓ 80 23.c even 11 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(10\!\cdots\!82\)\( T_{2}^{52} + 548706916315 T_{2}^{51} + \)\(41\!\cdots\!06\)\( T_{2}^{50} + 608694148183 T_{2}^{49} + \)\(16\!\cdots\!89\)\( T_{2}^{48} - \)\(48\!\cdots\!65\)\( T_{2}^{47} + \)\(59\!\cdots\!57\)\( T_{2}^{46} - \)\(35\!\cdots\!09\)\( T_{2}^{45} + \)\(17\!\cdots\!94\)\( T_{2}^{44} - \)\(17\!\cdots\!61\)\( T_{2}^{43} + \)\(52\!\cdots\!25\)\( T_{2}^{42} - \)\(47\!\cdots\!84\)\( T_{2}^{41} + \)\(12\!\cdots\!37\)\( T_{2}^{40} - \)\(14\!\cdots\!25\)\( T_{2}^{39} + \)\(28\!\cdots\!09\)\( T_{2}^{38} - \)\(40\!\cdots\!68\)\( T_{2}^{37} + \)\(84\!\cdots\!60\)\( T_{2}^{36} - \)\(14\!\cdots\!66\)\( T_{2}^{35} + \)\(26\!\cdots\!94\)\( T_{2}^{34} - \)\(38\!\cdots\!73\)\( T_{2}^{33} + \)\(64\!\cdots\!66\)\( T_{2}^{32} - \)\(87\!\cdots\!52\)\( T_{2}^{31} + \)\(14\!\cdots\!61\)\( T_{2}^{30} - \)\(22\!\cdots\!86\)\( T_{2}^{29} + \)\(39\!\cdots\!49\)\( T_{2}^{28} - \)\(54\!\cdots\!41\)\( T_{2}^{27} + \)\(67\!\cdots\!23\)\( T_{2}^{26} - \)\(80\!\cdots\!65\)\( T_{2}^{25} + \)\(85\!\cdots\!36\)\( T_{2}^{24} - \)\(87\!\cdots\!19\)\( T_{2}^{23} + \)\(84\!\cdots\!28\)\( T_{2}^{22} - \)\(56\!\cdots\!04\)\( T_{2}^{21} + \)\(40\!\cdots\!61\)\( T_{2}^{20} - \)\(16\!\cdots\!68\)\( T_{2}^{19} + \)\(60\!\cdots\!79\)\( T_{2}^{18} + \)\(71\!\cdots\!51\)\( T_{2}^{17} - \)\(88\!\cdots\!23\)\( T_{2}^{16} + \)\(46\!\cdots\!59\)\( T_{2}^{15} + \)\(23\!\cdots\!34\)\( T_{2}^{14} - \)\(17\!\cdots\!74\)\( T_{2}^{13} + \)\(88\!\cdots\!33\)\( T_{2}^{12} - \)\(10\!\cdots\!60\)\( T_{2}^{11} - \)\(47\!\cdots\!77\)\( T_{2}^{10} + \)\(43\!\cdots\!87\)\( T_{2}^{9} - \)\(30\!\cdots\!41\)\( T_{2}^{8} + \)\(26\!\cdots\!84\)\( T_{2}^{7} + \)\(80\!\cdots\!45\)\( T_{2}^{6} - \)\(25\!\cdots\!85\)\( T_{2}^{5} + 699886407536 T_{2}^{4} - 61711045204 T_{2}^{3} + 3693073622 T_{2}^{2} - 115009453 T_{2} + 2374681 \)">\(T_{2}^{80} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(483, [\chi])\).