Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6029,2,Mod(1,6029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6029 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6029.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: | \(48.1418073786\) |
Analytic rank: | \(0\) |
Dimension: | \(268\) |
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 | −2.82279 | 1.45736 | 5.96816 | −4.32160 | −4.11382 | −2.12666 | −11.2013 | −0.876107 | 12.1990 | ||||||||||||||||||
1.2 | −2.79474 | −0.330575 | 5.81059 | −0.623259 | 0.923873 | −2.39329 | −10.6496 | −2.89072 | 1.74185 | ||||||||||||||||||
1.3 | −2.76630 | −1.88876 | 5.65241 | −2.53163 | 5.22487 | 3.60505 | −10.1037 | 0.567402 | 7.00325 | ||||||||||||||||||
1.4 | −2.76187 | −2.45998 | 5.62792 | 2.94480 | 6.79415 | 1.83308 | −10.0198 | 3.05151 | −8.13315 | ||||||||||||||||||
1.5 | −2.74676 | 2.86871 | 5.54471 | 2.35059 | −7.87968 | 4.12455 | −9.73648 | 5.22952 | −6.45653 | ||||||||||||||||||
1.6 | −2.73508 | 2.32253 | 5.48068 | −2.83868 | −6.35232 | −0.0775144 | −9.51993 | 2.39417 | 7.76402 | ||||||||||||||||||
1.7 | −2.71891 | −2.75648 | 5.39247 | −2.65361 | 7.49462 | −3.09784 | −9.22383 | 4.59818 | 7.21494 | ||||||||||||||||||
1.8 | −2.69661 | 0.0652072 | 5.27173 | −0.769773 | −0.175839 | 2.92622 | −8.82260 | −2.99575 | 2.07578 | ||||||||||||||||||
1.9 | −2.67015 | 2.28839 | 5.12969 | 1.33703 | −6.11033 | −2.43023 | −8.35672 | 2.23672 | −3.57008 | ||||||||||||||||||
1.10 | −2.66582 | −1.97296 | 5.10658 | 1.39801 | 5.25954 | −2.57413 | −8.28157 | 0.892553 | −3.72685 | ||||||||||||||||||
1.11 | −2.66314 | 1.33494 | 5.09234 | −1.13177 | −3.55514 | 4.13938 | −8.23535 | −1.21793 | 3.01407 | ||||||||||||||||||
1.12 | −2.66122 | 1.83704 | 5.08208 | −0.683386 | −4.88877 | 2.95312 | −8.20207 | 0.374729 | 1.81864 | ||||||||||||||||||
1.13 | −2.65863 | −3.04392 | 5.06833 | −3.14510 | 8.09266 | 2.18672 | −8.15755 | 6.26543 | 8.36165 | ||||||||||||||||||
1.14 | −2.64287 | 3.18125 | 4.98477 | 0.556594 | −8.40764 | −4.05191 | −7.88836 | 7.12036 | −1.47101 | ||||||||||||||||||
1.15 | −2.64062 | −0.800557 | 4.97285 | 2.95022 | 2.11396 | 2.31379 | −7.85015 | −2.35911 | −7.79040 | ||||||||||||||||||
1.16 | −2.62126 | −0.553016 | 4.87101 | −3.94850 | 1.44960 | 2.94765 | −7.52568 | −2.69417 | 10.3501 | ||||||||||||||||||
1.17 | −2.54540 | −3.20721 | 4.47904 | 0.372386 | 8.16363 | −2.83053 | −6.31014 | 7.28621 | −0.947871 | ||||||||||||||||||
1.18 | −2.51173 | −2.30209 | 4.30878 | −2.37349 | 5.78222 | −4.88111 | −5.79902 | 2.29960 | 5.96156 | ||||||||||||||||||
1.19 | −2.51050 | 0.264508 | 4.30262 | 3.31299 | −0.664049 | 1.39465 | −5.78073 | −2.93004 | −8.31726 | ||||||||||||||||||
1.20 | −2.50934 | −1.29295 | 4.29679 | −2.86314 | 3.24445 | 3.23051 | −5.76344 | −1.32829 | 7.18460 | ||||||||||||||||||
See next 80 embeddings (of 268 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(6029\) | \(-1\) |
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 | 6029.2.a.b | ✓ | 268 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6029.2.a.b | ✓ | 268 | 1.a | even | 1 | 1 | trivial |