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: | \(0\) |
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 | −3.44578 | 0 | 2.15177 | 0 | 0.876792 | 0 | 8.87339 | 0 | ||||||||||||||||||
1.2 | 0 | −3.26383 | 0 | −4.12384 | 0 | −1.32793 | 0 | 7.65258 | 0 | ||||||||||||||||||
1.3 | 0 | −2.94078 | 0 | −0.581492 | 0 | −3.80526 | 0 | 5.64819 | 0 | ||||||||||||||||||
1.4 | 0 | −2.79559 | 0 | 1.54493 | 0 | 3.97273 | 0 | 4.81535 | 0 | ||||||||||||||||||
1.5 | 0 | −2.69290 | 0 | −2.32986 | 0 | −1.27542 | 0 | 4.25169 | 0 | ||||||||||||||||||
1.6 | 0 | −2.68247 | 0 | 0.714038 | 0 | 3.91380 | 0 | 4.19563 | 0 | ||||||||||||||||||
1.7 | 0 | −2.63352 | 0 | −1.02766 | 0 | −1.79528 | 0 | 3.93544 | 0 | ||||||||||||||||||
1.8 | 0 | −2.56682 | 0 | 0.554911 | 0 | −3.08439 | 0 | 3.58855 | 0 | ||||||||||||||||||
1.9 | 0 | −2.50519 | 0 | −1.30564 | 0 | 3.79113 | 0 | 3.27598 | 0 | ||||||||||||||||||
1.10 | 0 | −2.38781 | 0 | 2.32923 | 0 | 0.907839 | 0 | 2.70165 | 0 | ||||||||||||||||||
1.11 | 0 | −2.30919 | 0 | 2.96511 | 0 | 1.31242 | 0 | 2.33234 | 0 | ||||||||||||||||||
1.12 | 0 | −2.24731 | 0 | 0.981673 | 0 | −2.98823 | 0 | 2.05038 | 0 | ||||||||||||||||||
1.13 | 0 | −2.22958 | 0 | −3.12332 | 0 | 0.924225 | 0 | 1.97105 | 0 | ||||||||||||||||||
1.14 | 0 | −2.12225 | 0 | −0.499336 | 0 | −0.0909608 | 0 | 1.50393 | 0 | ||||||||||||||||||
1.15 | 0 | −2.06433 | 0 | 4.18134 | 0 | 5.19775 | 0 | 1.26148 | 0 | ||||||||||||||||||
1.16 | 0 | −1.67900 | 0 | −4.00186 | 0 | 3.70926 | 0 | −0.180962 | 0 | ||||||||||||||||||
1.17 | 0 | −1.55218 | 0 | −1.58422 | 0 | −1.70170 | 0 | −0.590736 | 0 | ||||||||||||||||||
1.18 | 0 | −1.47185 | 0 | −3.39845 | 0 | 2.90753 | 0 | −0.833657 | 0 | ||||||||||||||||||
1.19 | 0 | −1.08193 | 0 | −0.304592 | 0 | −4.98661 | 0 | −1.82943 | 0 | ||||||||||||||||||
1.20 | 0 | −1.07770 | 0 | 3.26525 | 0 | −1.02333 | 0 | −1.83857 | 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.b | ✓ | 63 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6044.2.a.b | ✓ | 63 | 1.a | even | 1 | 1 | trivial |