Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6044,2,Mod(1,6044)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6044, 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("6044.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6044 = 2^{2} \cdot 1511 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6044.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: | \(48.2615829817\) |
Analytic rank: | \(1\) |
Dimension: | \(63\) |
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 | 0 | −3.43683 | 0 | 1.31396 | 0 | 2.97589 | 0 | 8.81178 | 0 | ||||||||||||||||||
1.2 | 0 | −3.31051 | 0 | 0.0245297 | 0 | −4.08379 | 0 | 7.95946 | 0 | ||||||||||||||||||
1.3 | 0 | −3.15665 | 0 | −3.22660 | 0 | 1.21507 | 0 | 6.96442 | 0 | ||||||||||||||||||
1.4 | 0 | −3.10897 | 0 | 4.27127 | 0 | −2.96851 | 0 | 6.66567 | 0 | ||||||||||||||||||
1.5 | 0 | −3.06921 | 0 | 2.30904 | 0 | −0.616615 | 0 | 6.42006 | 0 | ||||||||||||||||||
1.6 | 0 | −2.97134 | 0 | −2.23756 | 0 | 4.75272 | 0 | 5.82886 | 0 | ||||||||||||||||||
1.7 | 0 | −2.95257 | 0 | −0.800433 | 0 | −2.68929 | 0 | 5.71766 | 0 | ||||||||||||||||||
1.8 | 0 | −2.59590 | 0 | −0.0339717 | 0 | 0.331169 | 0 | 3.73871 | 0 | ||||||||||||||||||
1.9 | 0 | −2.53520 | 0 | −2.05681 | 0 | 1.80178 | 0 | 3.42722 | 0 | ||||||||||||||||||
1.10 | 0 | −2.53490 | 0 | 4.14677 | 0 | 1.26365 | 0 | 3.42570 | 0 | ||||||||||||||||||
1.11 | 0 | −2.46300 | 0 | −1.99757 | 0 | 3.35645 | 0 | 3.06637 | 0 | ||||||||||||||||||
1.12 | 0 | −2.40035 | 0 | 2.30377 | 0 | −2.94550 | 0 | 2.76170 | 0 | ||||||||||||||||||
1.13 | 0 | −2.33939 | 0 | 2.09632 | 0 | 1.25063 | 0 | 2.47276 | 0 | ||||||||||||||||||
1.14 | 0 | −1.98161 | 0 | −3.75516 | 0 | −4.03693 | 0 | 0.926797 | 0 | ||||||||||||||||||
1.15 | 0 | −1.75230 | 0 | −3.12629 | 0 | −3.74178 | 0 | 0.0705422 | 0 | ||||||||||||||||||
1.16 | 0 | −1.69210 | 0 | −3.14690 | 0 | −4.59556 | 0 | −0.136814 | 0 | ||||||||||||||||||
1.17 | 0 | −1.68302 | 0 | 3.28650 | 0 | −4.68087 | 0 | −0.167449 | 0 | ||||||||||||||||||
1.18 | 0 | −1.59751 | 0 | 1.94100 | 0 | −3.58958 | 0 | −0.447960 | 0 | ||||||||||||||||||
1.19 | 0 | −1.58770 | 0 | −0.675402 | 0 | −1.82211 | 0 | −0.479212 | 0 | ||||||||||||||||||
1.20 | 0 | −1.57704 | 0 | 3.78585 | 0 | 1.51605 | 0 | −0.512930 | 0 | ||||||||||||||||||
See all 63 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(-1\) |
\(1511\) | \(-1\) |
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 | 6044.2.a.a | ✓ | 63 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6044.2.a.a | ✓ | 63 | 1.a | even | 1 | 1 | trivial |