Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8031,2,Mod(1,8031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8031, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8031 = 3 \cdot 2677 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8031.a (trivial) |
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: | yes |
Analytic conductor: | \(64.1278578633\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
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.
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1.1 | −2.78421 | −1.00000 | 5.75185 | 0.686525 | 2.78421 | −0.869505 | −10.4459 | 1.00000 | −1.91143 | ||||||||||||||||||
1.2 | −2.74757 | −1.00000 | 5.54913 | 2.21252 | 2.74757 | −1.55769 | −9.75147 | 1.00000 | −6.07904 | ||||||||||||||||||
1.3 | −2.68356 | −1.00000 | 5.20147 | −3.95156 | 2.68356 | −4.75750 | −8.59132 | 1.00000 | 10.6042 | ||||||||||||||||||
1.4 | −2.64556 | −1.00000 | 4.99897 | −1.40412 | 2.64556 | −0.985442 | −7.93394 | 1.00000 | 3.71467 | ||||||||||||||||||
1.5 | −2.62963 | −1.00000 | 4.91495 | 3.86074 | 2.62963 | 3.78778 | −7.66525 | 1.00000 | −10.1523 | ||||||||||||||||||
1.6 | −2.60983 | −1.00000 | 4.81123 | 0.810523 | 2.60983 | −4.83270 | −7.33685 | 1.00000 | −2.11533 | ||||||||||||||||||
1.7 | −2.47165 | −1.00000 | 4.10906 | −0.0868982 | 2.47165 | −4.58387 | −5.21287 | 1.00000 | 0.214782 | ||||||||||||||||||
1.8 | −2.46498 | −1.00000 | 4.07611 | 3.49515 | 2.46498 | 1.81173 | −5.11755 | 1.00000 | −8.61546 | ||||||||||||||||||
1.9 | −2.44537 | −1.00000 | 3.97985 | 0.860526 | 2.44537 | −1.02072 | −4.84146 | 1.00000 | −2.10431 | ||||||||||||||||||
1.10 | −2.41661 | −1.00000 | 3.83999 | −2.56069 | 2.41661 | −0.401342 | −4.44652 | 1.00000 | 6.18818 | ||||||||||||||||||
1.11 | −2.39891 | −1.00000 | 3.75476 | −1.21800 | 2.39891 | −2.25601 | −4.20952 | 1.00000 | 2.92186 | ||||||||||||||||||
1.12 | −2.36975 | −1.00000 | 3.61573 | −1.85498 | 2.36975 | 4.52062 | −3.82888 | 1.00000 | 4.39585 | ||||||||||||||||||
1.13 | −2.36162 | −1.00000 | 3.57726 | 0.566306 | 2.36162 | 3.15276 | −3.72490 | 1.00000 | −1.33740 | ||||||||||||||||||
1.14 | −2.35691 | −1.00000 | 3.55501 | 3.33677 | 2.35691 | −1.10286 | −3.66500 | 1.00000 | −7.86445 | ||||||||||||||||||
1.15 | −2.31301 | −1.00000 | 3.35001 | −2.44479 | 2.31301 | −2.31166 | −3.12259 | 1.00000 | 5.65482 | ||||||||||||||||||
1.16 | −2.29229 | −1.00000 | 3.25458 | 1.65455 | 2.29229 | 2.03484 | −2.87586 | 1.00000 | −3.79270 | ||||||||||||||||||
1.17 | −2.27538 | −1.00000 | 3.17734 | −2.29093 | 2.27538 | 1.46815 | −2.67889 | 1.00000 | 5.21272 | ||||||||||||||||||
1.18 | −2.15810 | −1.00000 | 2.65739 | −1.43595 | 2.15810 | 1.17187 | −1.41872 | 1.00000 | 3.09891 | ||||||||||||||||||
1.19 | −2.11893 | −1.00000 | 2.48988 | 3.42435 | 2.11893 | −4.49601 | −1.03803 | 1.00000 | −7.25596 | ||||||||||||||||||
1.20 | −1.99295 | −1.00000 | 1.97186 | 0.956056 | 1.99295 | 2.24151 | 0.0560744 | 1.00000 | −1.90538 | ||||||||||||||||||
See next 80 embeddings (of 121 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(1\) |
\(2677\) | \(-1\) |
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 | 8031.2.a.c | ✓ | 121 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8031.2.a.c | ✓ | 121 | 1.a | even | 1 | 1 | trivial |