Properties

Label 547.4.a.b
Level 547
Weight 4
Character orbit 547.a
Self dual yes
Analytic conductor 32.274
Analytic rank 0
Dimension 71
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: \(0\)
Dimension: \(71\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 71q + 14q^{2} + 31q^{3} + 294q^{4} + 159q^{5} + 60q^{6} + 66q^{7} + 168q^{8} + 738q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 71q + 14q^{2} + 31q^{3} + 294q^{4} + 159q^{5} + 60q^{6} + 66q^{7} + 168q^{8} + 738q^{9} + 120q^{10} + 139q^{11} + 309q^{12} + 343q^{13} + 239q^{14} + 194q^{15} + 1346q^{16} + 842q^{17} + 423q^{18} + 157q^{19} + 1292q^{20} + 434q^{21} + 436q^{22} + 1004q^{23} + 935q^{24} + 2206q^{25} + 812q^{26} + 1282q^{27} + 584q^{28} + 1459q^{29} + 146q^{30} + 582q^{31} + 1428q^{32} + 1080q^{33} + 393q^{34} + 1006q^{35} + 2996q^{36} + 1477q^{37} + 1873q^{38} + 626q^{39} + 1272q^{40} + 1112q^{41} + 1812q^{42} + 833q^{43} + 1392q^{44} + 3841q^{45} + 782q^{46} + 2484q^{47} + 2034q^{48} + 4727q^{49} + 1248q^{50} + 932q^{51} + 2118q^{52} + 5077q^{53} + 1537q^{54} + 1736q^{55} + 2281q^{56} + 1426q^{57} + 992q^{58} + 2977q^{59} + 1418q^{60} + 3363q^{61} + 3438q^{62} + 3194q^{63} + 6138q^{64} + 4640q^{65} + 288q^{66} + 955q^{67} + 8553q^{68} + 4440q^{69} + 2203q^{70} + 2458q^{71} + 4495q^{72} + 3724q^{73} + 2099q^{74} + 4491q^{75} + 2260q^{76} + 9774q^{77} + 1057q^{78} + 1638q^{79} + 8221q^{80} + 10151q^{81} + 1018q^{82} + 6121q^{83} + 4847q^{84} + 3836q^{85} + 2305q^{86} + 3894q^{87} + 5815q^{88} + 8110q^{89} + 4951q^{90} + 2312q^{91} + 13138q^{92} + 9250q^{93} - 813q^{94} + 4858q^{95} + 6882q^{96} + 4486q^{97} + 4216q^{98} + 4969q^{99} + O(q^{100}) \)

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 −5.33809 −2.63104 20.4952 12.8347 14.0448 22.5520 −66.7005 −20.0776 −68.5130
1.2 −5.26364 −3.16796 19.7059 21.3074 16.6750 −14.9641 −61.6156 −16.9640 −112.154
1.3 −5.16402 −8.74896 18.6671 −2.06725 45.1798 −11.4836 −55.0849 49.5444 10.6753
1.4 −5.16082 9.40532 18.6341 −10.9794 −48.5392 −11.5228 −54.8805 61.4600 56.6629
1.5 −5.04533 −1.70191 17.4553 1.56697 8.58669 −17.5256 −47.7054 −24.1035 −7.90590
1.6 −4.93277 2.64687 16.3322 −3.58160 −13.0564 9.94238 −41.1009 −19.9941 17.6672
1.7 −4.85758 9.04814 15.5961 16.7670 −43.9521 18.8884 −36.8987 54.8688 −81.4469
1.8 −4.68521 2.05946 13.9512 16.8174 −9.64900 3.12603 −27.8825 −22.7586 −78.7929
1.9 −4.65518 −5.82218 13.6707 −6.25020 27.1033 −2.07510 −26.3983 6.89779 29.0958
1.10 −4.53918 −1.35981 12.6041 −14.6057 6.17242 5.88252 −20.8990 −25.1509 66.2981
1.11 −4.13291 8.01594 9.08096 −4.43214 −33.1292 17.8969 −4.46750 37.2553 18.3177
1.12 −4.00233 4.42663 8.01862 −17.4366 −17.7168 −28.8522 −0.0745319 −7.40492 69.7871
1.13 −3.65756 −5.29226 5.37772 15.7763 19.3567 −21.1834 9.59114 1.00804 −57.7027
1.14 −3.61662 5.98739 5.07997 14.5299 −21.6541 21.3024 10.5606 8.84881 −52.5491
1.15 −3.45260 −9.18913 3.92046 −10.5912 31.7264 24.4389 14.0850 57.4401 36.5672
1.16 −3.19990 5.94033 2.23933 −4.08668 −19.0084 −18.1886 18.4335 8.28747 13.0769
1.17 −3.17215 −0.466644 2.06251 −2.33487 1.48026 −2.84434 18.8346 −26.7822 7.40655
1.18 −3.00219 −8.77445 1.01316 −10.0921 26.3426 −3.02021 20.9758 49.9910 30.2985
1.19 −2.54195 10.1442 −1.53851 19.6797 −25.7861 −26.4188 24.2464 75.9054 −50.0248
1.20 −2.30656 0.950194 −2.67977 −5.29729 −2.19168 32.9235 24.6336 −26.0971 12.2185
See all 71 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.71
Significant digits:
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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.b 71
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
547.4.a.b 71 1.a even 1 1 trivial

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database