Properties

Label 547.2.c.a
Level 547
Weight 2
Character orbit 547.c
Analytic conductor 4.368
Analytic rank 0
Dimension 90
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 547.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.36781699056\)
Analytic rank: \(0\)
Dimension: \(90\)
Relative dimension: \(45\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 90q - q^{2} - 4q^{3} - 47q^{4} + q^{5} - 3q^{6} + 2q^{7} - 30q^{8} + 82q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 90q - q^{2} - 4q^{3} - 47q^{4} + q^{5} - 3q^{6} + 2q^{7} - 30q^{8} + 82q^{9} - 10q^{10} + q^{11} + 4q^{12} - 3q^{13} + 2q^{14} - 7q^{15} - 39q^{16} - 4q^{17} - 11q^{18} - 2q^{19} + 25q^{20} - 27q^{21} - 7q^{22} + q^{23} + 32q^{24} - 40q^{25} - 10q^{26} - 34q^{27} - 28q^{28} + 26q^{29} - 40q^{30} - 24q^{31} + 19q^{32} + q^{33} - 6q^{34} - 8q^{35} - 36q^{36} - 10q^{37} + 24q^{38} + 22q^{39} + 20q^{40} + 3q^{41} + 38q^{42} - 12q^{43} - 30q^{44} - 2q^{45} - 40q^{46} + 32q^{47} + 14q^{48} - 43q^{49} + 14q^{50} + 13q^{51} + 46q^{52} + 9q^{53} - 8q^{54} + 4q^{55} - 8q^{56} - 8q^{57} + 4q^{58} + 22q^{59} - 2q^{60} - 12q^{61} + 11q^{62} + 8q^{63} + 22q^{64} + 18q^{65} + 12q^{66} - 22q^{67} + 6q^{68} - q^{69} - 6q^{70} - 4q^{71} - 140q^{72} + 17q^{73} + 17q^{74} + 39q^{75} + 84q^{76} - 4q^{77} + 33q^{78} - 72q^{79} - 40q^{80} + 18q^{81} - 9q^{82} + 24q^{83} + 114q^{84} + 40q^{85} - 72q^{86} - 78q^{87} - 22q^{88} + 14q^{89} + 96q^{90} - 8q^{92} - 76q^{93} + 108q^{94} - 11q^{95} - 34q^{96} - 74q^{98} - 62q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
40.1 −1.33767 2.31692i 0.0966282 −2.57874 + 4.46650i 1.37326 2.37856i −0.129257 0.223879i 1.47773 + 2.55950i 8.44732 −2.99066 −7.34791
40.2 −1.29191 2.23766i −2.49350 −2.33807 + 4.04966i −1.20490 + 2.08695i 3.22138 + 5.57959i −0.153516 0.265897i 6.91467 3.21753 6.22651
40.3 −1.27030 2.20022i 2.62364 −2.22732 + 3.85783i 1.37642 2.38403i −3.33280 5.77259i −0.989588 1.71402i 6.23624 3.88348 −6.99387
40.4 −1.25404 2.17206i 1.97245 −2.14522 + 3.71563i −0.855667 + 1.48206i −2.47352 4.28427i −0.491655 0.851571i 5.74459 0.890547 4.29215
40.5 −1.22561 2.12281i −0.689967 −2.00423 + 3.47142i 0.697521 1.20814i 0.845629 + 1.46467i 0.230510 + 0.399255i 4.92316 −2.52395 −3.41955
40.6 −1.03824 1.79828i −3.24819 −1.15587 + 2.00202i 1.45522 2.52051i 3.37239 + 5.84114i −1.02195 1.77008i 0.647316 7.55072 −6.04345
40.7 −0.983266 1.70307i −1.20089 −0.933624 + 1.61708i −1.27061 + 2.20077i 1.18080 + 2.04520i −0.342982 0.594062i −0.261060 −1.55785 4.99741
40.8 −0.981507 1.70002i 0.337082 −0.926713 + 1.60511i −0.170480 + 0.295281i −0.330849 0.573047i 2.30708 + 3.99598i −0.287726 −2.88638 0.669311
40.9 −0.958903 1.66087i −2.13159 −0.838990 + 1.45317i 0.601954 1.04261i 2.04398 + 3.54028i 0.787639 + 1.36423i −0.617573 1.54366 −2.30886
40.10 −0.949891 1.64526i 1.78362 −0.804585 + 1.39358i −1.75830 + 3.04546i −1.69424 2.93451i −0.768952 1.33186i −0.742491 0.181290 6.68076
40.11 −0.910411 1.57688i 2.60123 −0.657698 + 1.13917i −0.415434 + 0.719553i −2.36819 4.10182i 2.45287 + 4.24850i −1.24654 3.76638 1.51286
40.12 −0.842770 1.45972i 0.180635 −0.420521 + 0.728364i 0.214189 0.370986i −0.152234 0.263676i −2.38612 4.13289i −1.95347 −2.96737 −0.722047
40.13 −0.771252 1.33585i −0.116598 −0.189661 + 0.328502i 1.94811 3.37423i 0.0899263 + 0.155757i −1.20784 2.09204i −2.49991 −2.98640 −6.00995
40.14 −0.701193 1.21450i 2.83551 0.0166570 0.0288508i 1.44371 2.50058i −1.98824 3.44374i 0.560388 + 0.970620i −2.85149 5.04014 −4.04928
40.15 −0.557049 0.964838i −2.42664 0.379392 0.657126i 1.11858 1.93744i 1.35176 + 2.34132i 1.58983 + 2.75366i −3.07356 2.88859 −2.49243
40.16 −0.467669 0.810027i 3.30105 0.562571 0.974402i −0.395260 + 0.684610i −1.54380 2.67394i −2.17986 3.77563i −2.92307 7.89696 0.739403
40.17 −0.462183 0.800525i −2.33209 0.572774 0.992073i −1.08506 + 1.87939i 1.07785 + 1.86689i −1.53583 2.66014i −2.90764 2.43863 2.00599
40.18 −0.439469 0.761182i −3.32207 0.613734 1.06302i −1.74661 + 3.02521i 1.45994 + 2.52870i 2.14689 + 3.71852i −2.83674 8.03612 3.07032
40.19 −0.364678 0.631642i 1.05712 0.734019 1.27136i 0.718385 1.24428i −0.385510 0.667723i −0.0543155 0.0940772i −2.52944 −1.88249 −1.04792
40.20 −0.342487 0.593205i −0.609933 0.765405 1.32572i −0.502260 + 0.869940i 0.208894 + 0.361815i 1.02901 + 1.78229i −2.41851 −2.62798 0.688071
See all 90 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 506.45
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
547.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 547.2.c.a 90
547.c even 3 1 inner 547.2.c.a 90
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
547.2.c.a 90 1.a even 1 1 trivial
547.2.c.a 90 547.c even 3 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(547, [\chi])\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database