Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6035,2,Mod(1,6035)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6035, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6035.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6035 = 5 \cdot 17 \cdot 71 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6035.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: | \(48.1897176198\) |
Analytic rank: | \(0\) |
Dimension: | \(58\) |
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 | −2.80026 | 1.99842 | 5.84147 | 1.00000 | −5.59610 | −4.62775 | −10.7571 | 0.993679 | −2.80026 | ||||||||||||||||||
1.2 | −2.75680 | 2.57899 | 5.59996 | 1.00000 | −7.10976 | 3.29093 | −9.92438 | 3.65117 | −2.75680 | ||||||||||||||||||
1.3 | −2.70439 | −2.73763 | 5.31370 | 1.00000 | 7.40360 | −4.83847 | −8.96152 | 4.49461 | −2.70439 | ||||||||||||||||||
1.4 | −2.68796 | −2.40870 | 5.22515 | 1.00000 | 6.47449 | 1.33386 | −8.66909 | 2.80181 | −2.68796 | ||||||||||||||||||
1.5 | −2.49259 | −0.124755 | 4.21303 | 1.00000 | 0.310963 | 1.75866 | −5.51618 | −2.98444 | −2.49259 | ||||||||||||||||||
1.6 | −2.45480 | −1.45794 | 4.02604 | 1.00000 | 3.57896 | −2.38415 | −4.97353 | −0.874405 | −2.45480 | ||||||||||||||||||
1.7 | −2.40526 | 1.86065 | 3.78528 | 1.00000 | −4.47536 | 2.19847 | −4.29406 | 0.462037 | −2.40526 | ||||||||||||||||||
1.8 | −2.20983 | 3.43880 | 2.88333 | 1.00000 | −7.59915 | −1.16489 | −1.95201 | 8.82536 | −2.20983 | ||||||||||||||||||
1.9 | −2.17363 | 0.623249 | 2.72466 | 1.00000 | −1.35471 | −4.14588 | −1.57514 | −2.61156 | −2.17363 | ||||||||||||||||||
1.10 | −2.15077 | −3.16911 | 2.62583 | 1.00000 | 6.81604 | −1.54855 | −1.34601 | 7.04327 | −2.15077 | ||||||||||||||||||
1.11 | −2.12400 | −1.09989 | 2.51137 | 1.00000 | 2.33617 | 5.15845 | −1.08615 | −1.79024 | −2.12400 | ||||||||||||||||||
1.12 | −2.00836 | 0.177134 | 2.03352 | 1.00000 | −0.355749 | −1.65376 | −0.0673116 | −2.96862 | −2.00836 | ||||||||||||||||||
1.13 | −1.83919 | 1.25269 | 1.38262 | 1.00000 | −2.30393 | 1.52576 | 1.13547 | −1.43078 | −1.83919 | ||||||||||||||||||
1.14 | −1.67839 | 3.22950 | 0.816985 | 1.00000 | −5.42036 | 0.934275 | 1.98556 | 7.42970 | −1.67839 | ||||||||||||||||||
1.15 | −1.56061 | −2.33055 | 0.435498 | 1.00000 | 3.63707 | 3.61265 | 2.44157 | 2.43146 | −1.56061 | ||||||||||||||||||
1.16 | −1.54425 | −3.31836 | 0.384710 | 1.00000 | 5.12438 | 3.26635 | 2.49441 | 8.01151 | −1.54425 | ||||||||||||||||||
1.17 | −1.51455 | 1.68592 | 0.293855 | 1.00000 | −2.55340 | −0.258342 | 2.58404 | −0.157685 | −1.51455 | ||||||||||||||||||
1.18 | −1.30337 | −0.487797 | −0.301228 | 1.00000 | 0.635780 | −1.77737 | 2.99935 | −2.76205 | −1.30337 | ||||||||||||||||||
1.19 | −1.22809 | 1.74628 | −0.491793 | 1.00000 | −2.14460 | 4.49008 | 3.06015 | 0.0495068 | −1.22809 | ||||||||||||||||||
1.20 | −1.22218 | −2.16829 | −0.506288 | 1.00000 | 2.65003 | −1.52570 | 3.06312 | 1.70146 | −1.22218 | ||||||||||||||||||
See all 58 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(5\) | \(-1\) |
\(17\) | \(-1\) |
\(71\) | \(-1\) |
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 | 6035.2.a.g | ✓ | 58 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6035.2.a.g | ✓ | 58 | 1.a | even | 1 | 1 | trivial |