Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [935,2,Mod(89,935)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(935, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("935.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 935 = 5 \cdot 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 935.s (of order \(4\), 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: | \(7.46601258899\) |
Analytic rank: | \(0\) |
Dimension: | \(176\) |
Relative dimension: | \(88\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
89.1 | −2.78286 | 1.11291 | + | 1.11291i | 5.74428 | −0.780852 | − | 2.09530i | −3.09707 | − | 3.09707i | 1.86351 | − | 1.86351i | −10.4198 | − | 0.522851i | 2.17300 | + | 5.83091i | |||||||
89.2 | −2.71389 | 1.08381 | + | 1.08381i | 5.36518 | −0.196718 | + | 2.22740i | −2.94135 | − | 2.94135i | −0.893035 | + | 0.893035i | −9.13272 | − | 0.650695i | 0.533870 | − | 6.04491i | |||||||
89.3 | −2.68198 | −1.48774 | − | 1.48774i | 5.19303 | −1.37789 | + | 1.76109i | 3.99008 | + | 3.99008i | 1.70185 | − | 1.70185i | −8.56365 | 1.42672i | 3.69547 | − | 4.72320i | ||||||||
89.4 | −2.60361 | −1.03941 | − | 1.03941i | 4.77880 | 2.06449 | + | 0.858995i | 2.70623 | + | 2.70623i | −0.436910 | + | 0.436910i | −7.23493 | − | 0.839245i | −5.37514 | − | 2.23649i | |||||||
89.5 | −2.54872 | 1.00064 | + | 1.00064i | 4.49595 | 2.21347 | + | 0.317109i | −2.55034 | − | 2.55034i | −0.462784 | + | 0.462784i | −6.36146 | − | 0.997457i | −5.64150 | − | 0.808221i | |||||||
89.6 | −2.48276 | −0.552169 | − | 0.552169i | 4.16409 | 1.20456 | − | 1.88389i | 1.37090 | + | 1.37090i | 2.12488 | − | 2.12488i | −5.37292 | − | 2.39022i | −2.99062 | + | 4.67725i | |||||||
89.7 | −2.46090 | 1.90829 | + | 1.90829i | 4.05603 | 1.00606 | − | 1.99696i | −4.69611 | − | 4.69611i | −3.35879 | + | 3.35879i | −5.05970 | 4.28312i | −2.47581 | + | 4.91432i | ||||||||
89.8 | −2.43106 | −0.953668 | − | 0.953668i | 3.91005 | −2.00582 | + | 0.988275i | 2.31842 | + | 2.31842i | 0.451938 | − | 0.451938i | −4.64343 | − | 1.18103i | 4.87627 | − | 2.40255i | |||||||
89.9 | −2.31180 | −1.72601 | − | 1.72601i | 3.34442 | 1.14866 | + | 1.91848i | 3.99019 | + | 3.99019i | −2.78193 | + | 2.78193i | −3.10803 | 2.95821i | −2.65547 | − | 4.43515i | ||||||||
89.10 | −2.29290 | −2.27659 | − | 2.27659i | 3.25738 | 2.12692 | − | 0.690070i | 5.21999 | + | 5.21999i | 2.42710 | − | 2.42710i | −2.88306 | 7.36573i | −4.87682 | + | 1.58226i | ||||||||
89.11 | −2.29290 | 0.332523 | + | 0.332523i | 3.25737 | −1.86965 | − | 1.22655i | −0.762439 | − | 0.762439i | −1.52018 | + | 1.52018i | −2.88302 | − | 2.77886i | 4.28691 | + | 2.81234i | |||||||
89.12 | −2.23685 | −1.31033 | − | 1.31033i | 3.00350 | −1.16908 | − | 1.90611i | 2.93101 | + | 2.93101i | −0.128790 | + | 0.128790i | −2.24467 | 0.433933i | 2.61505 | + | 4.26368i | ||||||||
89.13 | −2.11924 | 0.710313 | + | 0.710313i | 2.49120 | −2.21657 | + | 0.294649i | −1.50533 | − | 1.50533i | 3.33492 | − | 3.33492i | −1.04097 | − | 1.99091i | 4.69745 | − | 0.624434i | |||||||
89.14 | −2.08344 | 0.210181 | + | 0.210181i | 2.34072 | 0.240850 | + | 2.22306i | −0.437899 | − | 0.437899i | −2.18770 | + | 2.18770i | −0.709863 | − | 2.91165i | −0.501797 | − | 4.63161i | |||||||
89.15 | −2.07859 | 2.16490 | + | 2.16490i | 2.32052 | 1.59023 | + | 1.57199i | −4.49994 | − | 4.49994i | 1.14367 | − | 1.14367i | −0.666239 | 6.37360i | −3.30544 | − | 3.26753i | ||||||||
89.16 | −2.07526 | 1.11341 | + | 1.11341i | 2.30670 | 1.95717 | − | 1.08142i | −2.31061 | − | 2.31061i | 2.29464 | − | 2.29464i | −0.636478 | − | 0.520652i | −4.06164 | + | 2.24423i | |||||||
89.17 | −1.99798 | −2.26187 | − | 2.26187i | 1.99192 | −2.15822 | + | 0.584891i | 4.51917 | + | 4.51917i | −2.62923 | + | 2.62923i | 0.0161446 | 7.23211i | 4.31207 | − | 1.16860i | ||||||||
89.18 | −1.93920 | −0.202137 | − | 0.202137i | 1.76050 | 1.09642 | − | 1.94881i | 0.391984 | + | 0.391984i | −1.63995 | + | 1.63995i | 0.464433 | − | 2.91828i | −2.12617 | + | 3.77914i | |||||||
89.19 | −1.71101 | 0.318077 | + | 0.318077i | 0.927565 | −1.48521 | + | 1.67157i | −0.544233 | − | 0.544233i | 0.619417 | − | 0.619417i | 1.83495 | − | 2.79765i | 2.54122 | − | 2.86008i | |||||||
89.20 | −1.64074 | −1.91660 | − | 1.91660i | 0.692030 | −0.0332711 | + | 2.23582i | 3.14465 | + | 3.14465i | 2.09640 | − | 2.09640i | 2.14604 | 4.34672i | 0.0545892 | − | 3.66840i | ||||||||
See next 80 embeddings (of 176 total) |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
5.b | even | 2 | 1 | inner |
17.c | even | 4 | 1 | inner |
85.j | even | 4 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 935.2.s.a | ✓ | 176 |
5.b | even | 2 | 1 | inner | 935.2.s.a | ✓ | 176 |
17.c | even | 4 | 1 | inner | 935.2.s.a | ✓ | 176 |
85.j | even | 4 | 1 | inner | 935.2.s.a | ✓ | 176 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
935.2.s.a | ✓ | 176 | 1.a | even | 1 | 1 | trivial |
935.2.s.a | ✓ | 176 | 5.b | even | 2 | 1 | inner |
935.2.s.a | ✓ | 176 | 17.c | even | 4 | 1 | inner |
935.2.s.a | ✓ | 176 | 85.j | even | 4 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(935, [\chi])\).