Properties

Label 287.3.k.a
Level 287
Weight 3
Character orbit 287.k
Analytic conductor 7.820
Analytic rank 0
Dimension 108
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 287.k (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.82018358714\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(54\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 108q - 2q^{2} - 6q^{3} - 106q^{4} - 6q^{5} - 4q^{7} - 4q^{8} + 164q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 108q - 2q^{2} - 6q^{3} - 106q^{4} - 6q^{5} - 4q^{7} - 4q^{8} + 164q^{9} + 48q^{10} + 6q^{11} + 18q^{12} + 38q^{14} - 56q^{15} - 202q^{16} + 48q^{17} + 32q^{18} - 78q^{19} - 104q^{21} - 48q^{22} - 16q^{23} + 248q^{25} + 144q^{26} + 168q^{29} - 64q^{30} + 30q^{31} - 104q^{32} + 24q^{33} - 54q^{35} - 524q^{36} + 76q^{37} - 24q^{38} - 34q^{39} - 288q^{40} + 190q^{42} - 112q^{43} + 102q^{44} + 6q^{45} - 68q^{46} + 294q^{47} + 68q^{49} - 264q^{50} - 36q^{51} - 306q^{52} + 152q^{53} + 102q^{54} - 438q^{56} + 256q^{57} - 164q^{58} - 138q^{59} + 280q^{60} + 282q^{61} + 442q^{63} + 796q^{64} + 76q^{65} - 240q^{66} - 158q^{67} - 738q^{68} - 82q^{70} - 48q^{71} - 374q^{72} + 48q^{73} + 34q^{74} - 258q^{75} - 184q^{77} + 432q^{78} + 128q^{79} + 12q^{80} - 262q^{81} + 628q^{84} - 196q^{85} + 316q^{86} + 438q^{87} + 76q^{88} - 24q^{89} + 370q^{91} - 592q^{92} - 90q^{93} - 264q^{94} - 250q^{95} - 102q^{96} - 100q^{98} + 168q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
124.1 −1.93029 + 3.34336i −4.01504 + 2.31809i −5.45204 9.44321i −4.36678 2.52116i 17.8983i 1.27089 + 6.88366i 26.6537 6.24704 10.8202i 16.8583 9.73314i
124.2 −1.92489 + 3.33401i 1.96348 1.13362i −5.41042 9.37112i −7.92643 4.57633i 8.72835i −3.45956 6.08535i 26.2587 −1.92983 + 3.34256i 30.5151 17.6179i
124.3 −1.90578 + 3.30090i −0.0412365 + 0.0238079i −5.26396 9.11744i 6.03383 + 3.48363i 0.181490i −6.34884 2.94826i 24.8815 −4.49887 + 7.79227i −22.9983 + 13.2780i
124.4 −1.74836 + 3.02825i −0.731480 + 0.422320i −4.11352 7.12483i 1.70710 + 0.985597i 2.95347i 6.89618 1.20112i 14.7808 −4.14329 + 7.17639i −5.96926 + 3.44636i
124.5 −1.72365 + 2.98545i 3.56232 2.05671i −3.94194 6.82763i −2.71867 1.56963i 14.1802i 6.55146 + 2.46544i 13.3889 3.96008 6.85907i 9.37208 5.41098i
124.6 −1.68897 + 2.92538i 3.96120 2.28700i −3.70522 6.41763i 5.00681 + 2.89068i 15.4507i −1.27365 + 6.88315i 11.5203 5.96073 10.3243i −16.9127 + 9.76454i
124.7 −1.62412 + 2.81306i −4.24432 + 2.45046i −3.27555 5.67343i 2.25447 + 1.30162i 15.9194i 0.386365 6.98933i 8.28663 7.50952 13.0069i −7.32307 + 4.22798i
124.8 −1.53584 + 2.66015i 3.00422 1.73449i −2.71760 4.70703i −0.505558 0.291884i 10.6556i −6.85670 + 1.40915i 4.40850 1.51690 2.62735i 1.55291 0.896574i
124.9 −1.47349 + 2.55216i −1.81510 + 1.04795i −2.34234 4.05705i −2.56042 1.47826i 6.17655i −6.99953 + 0.0810157i 2.01773 −2.30362 + 3.98998i 7.54550 4.35639i
124.10 −1.44872 + 2.50926i −3.75993 + 2.17079i −2.19760 3.80636i 8.05382 + 4.64987i 12.5795i −2.97169 + 6.33790i 1.14508 4.92470 8.52983i −23.3355 + 13.4728i
124.11 −1.31543 + 2.27839i −0.740318 + 0.427423i −1.46069 2.52999i −2.81050 1.62264i 2.24897i −0.616116 + 6.97283i −2.83768 −4.13462 + 7.16137i 7.39401 4.26893i
124.12 −1.28731 + 2.22968i 2.52480 1.45770i −1.31432 2.27647i 6.56565 + 3.79068i 7.50600i 2.68275 6.46551i −3.53073 −0.250250 + 0.433446i −16.9040 + 9.75954i
124.13 −1.16522 + 2.01823i −1.57033 + 0.906633i −0.715498 1.23928i −8.48153 4.89681i 4.22573i 6.28605 3.07987i −5.98693 −2.85603 + 4.94679i 19.7658 11.4118i
124.14 −1.09053 + 1.88885i 1.31239 0.757706i −0.378493 0.655569i −2.19911 1.26966i 3.30519i 1.49325 6.83887i −7.07318 −3.35176 + 5.80542i 4.79637 2.76919i
124.15 −1.07150 + 1.85589i 4.93694 2.85034i −0.296226 0.513078i −2.71530 1.56768i 12.2166i −3.44147 6.09559i −7.30238 11.7489 20.3497i 5.81889 3.35954i
124.16 −0.981202 + 1.69949i −4.51577 + 2.60718i 0.0744841 + 0.129010i 0.831105 + 0.479839i 10.2327i 6.78912 + 1.70524i −8.14195 9.09481 15.7527i −1.63096 + 0.941637i
124.17 −0.817986 + 1.41679i 0.866025 0.500000i 0.661798 + 1.14627i 4.54885 + 2.62628i 1.63597i 2.81022 + 6.41114i −8.70925 −4.00000 + 6.92820i −7.44179 + 4.29652i
124.18 −0.790461 + 1.36912i −2.95293 + 1.70487i 0.750343 + 1.29963i 3.10718 + 1.79393i 5.39054i −0.932911 6.93756i −8.69615 1.31318 2.27450i −4.91222 + 2.83607i
124.19 −0.759629 + 1.31572i −4.86698 + 2.80995i 0.845927 + 1.46519i −7.28520 4.20611i 8.53809i −7.00000 0.00540808i −8.64740 11.2917 19.5577i 11.0681 6.39017i
124.20 −0.721947 + 1.25045i 3.30883 1.91036i 0.957585 + 1.65859i −6.47182 3.73651i 5.51670i 0.469222 + 6.98426i −8.54088 2.79891 4.84786i 9.34463 5.39512i
See next 80 embeddings (of 108 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 206.54
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.d odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 287.3.k.a 108
7.d odd 6 1 inner 287.3.k.a 108
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
287.3.k.a 108 1.a even 1 1 trivial
287.3.k.a 108 7.d odd 6 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(287, [\chi])\).