Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,3,Mod(124,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("287.124");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.k (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.82018358714\) |
Analytic rank: | \(0\) |
Dimension: | \(108\) |
Relative dimension: | \(54\) over \(\Q(\zeta_{6})\) |
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.
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.
comment: embeddings in the coefficient field
gp: mfembed(f)
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) |
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 \(S_{3}^{\mathrm{new}}(287, [\chi])\).