Properties

Label 547.4.a.a
Level 547
Weight 4
Character orbit 547.a
Self dual yes
Analytic conductor 32.274
Analytic rank 1
Dimension 65
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 547.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2740447731\)
Analytic rank: \(1\)
Dimension: \(65\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 65q - 12q^{2} - 35q^{3} + 234q^{4} - 151q^{5} - 60q^{6} - 74q^{7} - 144q^{8} + 468q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 65q - 12q^{2} - 35q^{3} + 234q^{4} - 151q^{5} - 60q^{6} - 74q^{7} - 144q^{8} + 468q^{9} - 60q^{10} - 191q^{11} - 483q^{12} - 333q^{13} - 377q^{14} - 166q^{15} + 818q^{16} - 858q^{17} - 279q^{18} - 185q^{19} - 1188q^{20} - 406q^{21} - 356q^{22} - 836q^{23} - 505q^{24} + 1156q^{25} - 696q^{26} - 1094q^{27} - 1096q^{28} - 1209q^{29} - 1054q^{30} - 286q^{31} - 1484q^{32} - 1296q^{33} - 763q^{34} - 1374q^{35} + 296q^{36} - 1705q^{37} - 2535q^{38} - 622q^{39} - 888q^{40} - 1348q^{41} - 1716q^{42} - 973q^{43} - 2568q^{44} - 4529q^{45} - 322q^{46} - 2498q^{47} - 5358q^{48} + 2081q^{49} - 2002q^{50} - 1108q^{51} - 3290q^{52} - 5947q^{53} - 2783q^{54} - 1344q^{55} - 5111q^{56} - 3134q^{57} - 1676q^{58} - 1625q^{59} - 2902q^{60} - 3103q^{61} - 5242q^{62} - 3106q^{63} + 1722q^{64} - 3160q^{65} - 3672q^{66} - 2395q^{67} - 8447q^{68} - 4944q^{69} - 597q^{70} - 2654q^{71} - 3929q^{72} - 2116q^{73} - 3969q^{74} - 3759q^{75} - 1844q^{76} - 9938q^{77} - 3935q^{78} - 1206q^{79} - 11619q^{80} + 1889q^{81} - 7674q^{82} - 4337q^{83} - 1873q^{84} - 2624q^{85} - 3543q^{86} - 3066q^{87} - 3689q^{88} - 5774q^{89} - 3149q^{90} - 3148q^{91} - 8942q^{92} - 7118q^{93} - 5137q^{94} - 2742q^{95} - 6558q^{96} - 6378q^{97} - 7250q^{98} - 3941q^{99} + O(q^{100}) \)

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 −5.63393 −0.244269 23.7412 −10.7943 1.37619 −27.5752 −88.6848 −26.9403 60.8146
1.2 −5.49091 4.91015 22.1501 0.763977 −26.9612 20.0589 −77.6972 −2.89047 −4.19493
1.3 −5.47859 −7.38039 22.0150 −19.6221 40.4341 27.6127 −76.7823 27.4701 107.502
1.4 −5.20814 −8.41779 19.1247 9.35810 43.8410 −4.06013 −57.9389 43.8592 −48.7383
1.5 −4.96544 7.58541 16.6556 8.10387 −37.6649 −24.7619 −42.9790 30.5385 −40.2393
1.6 −4.80997 5.25749 15.1358 −20.0143 −25.2884 11.4337 −34.3228 0.641223 96.2679
1.7 −4.72733 3.70224 14.3476 9.89284 −17.5017 −22.6244 −30.0072 −13.2934 −46.7667
1.8 −4.64265 −3.14883 13.5542 −12.0754 14.6189 −0.551526 −25.7864 −17.0849 56.0621
1.9 −4.53338 −4.26421 12.5516 3.96253 19.3313 35.0485 −20.6339 −8.81653 −17.9637
1.10 −4.39733 −7.45622 11.3366 −12.8080 32.7875 −33.9402 −14.6719 28.5953 56.3210
1.11 −4.22615 −9.49450 9.86034 11.9082 40.1252 16.0312 −7.86208 63.1455 −50.3258
1.12 −3.93855 1.10159 7.51219 5.92954 −4.33869 −15.7024 1.92127 −25.7865 −23.3538
1.13 −3.89720 3.45547 7.18817 −9.93922 −13.4667 29.7950 3.16387 −15.0597 38.7351
1.14 −3.59199 −5.98144 4.90240 5.54311 21.4853 −31.4038 11.1265 8.77766 −19.9108
1.15 −3.43782 −5.96032 3.81862 14.1232 20.4905 10.3663 14.3748 8.52547 −48.5529
1.16 −3.42061 −0.613467 3.70058 3.50938 2.09843 16.1360 14.7066 −26.6237 −12.0042
1.17 −3.41983 7.59300 3.69524 4.48488 −25.9668 −4.49298 14.7215 30.6536 −15.3375
1.18 −3.32782 9.69808 3.07435 −12.4114 −32.2734 29.0135 16.3916 67.0527 41.3030
1.19 −3.28242 2.93579 2.77430 18.0532 −9.63649 12.8406 17.1530 −18.3812 −59.2581
1.20 −3.05184 −4.83017 1.31373 −18.6497 14.7409 8.22006 20.4054 −3.66951 56.9157
See all 65 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.65
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(547\) \(-1\)

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 547.4.a.a 65
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
547.4.a.a 65 1.a even 1 1 trivial

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database