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: | \(132\) |
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 | −2.80398 | 1.00000 | 5.86231 | 1.87605 | −2.80398 | 3.15563 | −10.8299 | 1.00000 | −5.26041 | ||||||||||||||||||
1.2 | −2.77294 | 1.00000 | 5.68922 | −1.74396 | −2.77294 | 0.0730159 | −10.2300 | 1.00000 | 4.83589 | ||||||||||||||||||
1.3 | −2.75661 | 1.00000 | 5.59891 | −4.00125 | −2.75661 | −2.17438 | −9.92081 | 1.00000 | 11.0299 | ||||||||||||||||||
1.4 | −2.72616 | 1.00000 | 5.43195 | −1.18317 | −2.72616 | −4.48555 | −9.35605 | 1.00000 | 3.22552 | ||||||||||||||||||
1.5 | −2.69638 | 1.00000 | 5.27048 | 2.40729 | −2.69638 | −4.24108 | −8.81846 | 1.00000 | −6.49098 | ||||||||||||||||||
1.6 | −2.68578 | 1.00000 | 5.21342 | 1.21683 | −2.68578 | 2.10686 | −8.63055 | 1.00000 | −3.26813 | ||||||||||||||||||
1.7 | −2.67095 | 1.00000 | 5.13397 | −2.93949 | −2.67095 | 4.35242 | −8.37068 | 1.00000 | 7.85124 | ||||||||||||||||||
1.8 | −2.59180 | 1.00000 | 4.71742 | 2.79387 | −2.59180 | −2.04048 | −7.04300 | 1.00000 | −7.24116 | ||||||||||||||||||
1.9 | −2.57206 | 1.00000 | 4.61548 | 3.83645 | −2.57206 | −2.68797 | −6.72717 | 1.00000 | −9.86756 | ||||||||||||||||||
1.10 | −2.56954 | 1.00000 | 4.60252 | −1.45340 | −2.56954 | 2.82926 | −6.68726 | 1.00000 | 3.73456 | ||||||||||||||||||
1.11 | −2.55916 | 1.00000 | 4.54932 | −0.940256 | −2.55916 | 2.24269 | −6.52413 | 1.00000 | 2.40627 | ||||||||||||||||||
1.12 | −2.50203 | 1.00000 | 4.26014 | −3.95750 | −2.50203 | 1.89022 | −5.65494 | 1.00000 | 9.90177 | ||||||||||||||||||
1.13 | −2.48023 | 1.00000 | 4.15155 | 4.11076 | −2.48023 | 4.68191 | −5.33633 | 1.00000 | −10.1956 | ||||||||||||||||||
1.14 | −2.46874 | 1.00000 | 4.09466 | −2.24657 | −2.46874 | 4.89936 | −5.17116 | 1.00000 | 5.54618 | ||||||||||||||||||
1.15 | −2.45456 | 1.00000 | 4.02485 | −4.17412 | −2.45456 | −1.11531 | −4.97011 | 1.00000 | 10.2456 | ||||||||||||||||||
1.16 | −2.29731 | 1.00000 | 3.27764 | −1.75176 | −2.29731 | −2.80141 | −2.93514 | 1.00000 | 4.02433 | ||||||||||||||||||
1.17 | −2.23840 | 1.00000 | 3.01043 | 3.52664 | −2.23840 | 3.86222 | −2.26174 | 1.00000 | −7.89403 | ||||||||||||||||||
1.18 | −2.20104 | 1.00000 | 2.84456 | 0.313894 | −2.20104 | 1.59317 | −1.85890 | 1.00000 | −0.690891 | ||||||||||||||||||
1.19 | −2.19060 | 1.00000 | 2.79873 | 1.38696 | −2.19060 | −0.332475 | −1.74969 | 1.00000 | −3.03827 | ||||||||||||||||||
1.20 | −2.17916 | 1.00000 | 2.74876 | 2.82413 | −2.17916 | 4.47038 | −1.63167 | 1.00000 | −6.15424 | ||||||||||||||||||
See next 80 embeddings (of 132 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.d | ✓ | 132 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8031.2.a.d | ✓ | 132 | 1.a | even | 1 | 1 | trivial |