Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [547,4,Mod(1,547)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("547.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 547 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 547.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: | \(32.2740447731\) |
Analytic rank: | \(1\) |
Dimension: | \(65\) |
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 | −5.63393 | −0.244269 | 23.7412 | −10.7943 | 1.37619 | −27.5752 | −88.6848 | −26.9403 | 60.8146 | ||||||||||||||||||
1.2 | −5.49091 | 4.91015 | 22.1501 | 0.763977 | −26.9612 | 20.0589 | −77.6972 | −2.89047 | −4.19493 | ||||||||||||||||||
1.3 | −5.47859 | −7.38039 | 22.0150 | −19.6221 | 40.4341 | 27.6127 | −76.7823 | 27.4701 | 107.502 | ||||||||||||||||||
1.4 | −5.20814 | −8.41779 | 19.1247 | 9.35810 | 43.8410 | −4.06013 | −57.9389 | 43.8592 | −48.7383 | ||||||||||||||||||
1.5 | −4.96544 | 7.58541 | 16.6556 | 8.10387 | −37.6649 | −24.7619 | −42.9790 | 30.5385 | −40.2393 | ||||||||||||||||||
1.6 | −4.80997 | 5.25749 | 15.1358 | −20.0143 | −25.2884 | 11.4337 | −34.3228 | 0.641223 | 96.2679 | ||||||||||||||||||
1.7 | −4.72733 | 3.70224 | 14.3476 | 9.89284 | −17.5017 | −22.6244 | −30.0072 | −13.2934 | −46.7667 | ||||||||||||||||||
1.8 | −4.64265 | −3.14883 | 13.5542 | −12.0754 | 14.6189 | −0.551526 | −25.7864 | −17.0849 | 56.0621 | ||||||||||||||||||
1.9 | −4.53338 | −4.26421 | 12.5516 | 3.96253 | 19.3313 | 35.0485 | −20.6339 | −8.81653 | −17.9637 | ||||||||||||||||||
1.10 | −4.39733 | −7.45622 | 11.3366 | −12.8080 | 32.7875 | −33.9402 | −14.6719 | 28.5953 | 56.3210 | ||||||||||||||||||
1.11 | −4.22615 | −9.49450 | 9.86034 | 11.9082 | 40.1252 | 16.0312 | −7.86208 | 63.1455 | −50.3258 | ||||||||||||||||||
1.12 | −3.93855 | 1.10159 | 7.51219 | 5.92954 | −4.33869 | −15.7024 | 1.92127 | −25.7865 | −23.3538 | ||||||||||||||||||
1.13 | −3.89720 | 3.45547 | 7.18817 | −9.93922 | −13.4667 | 29.7950 | 3.16387 | −15.0597 | 38.7351 | ||||||||||||||||||
1.14 | −3.59199 | −5.98144 | 4.90240 | 5.54311 | 21.4853 | −31.4038 | 11.1265 | 8.77766 | −19.9108 | ||||||||||||||||||
1.15 | −3.43782 | −5.96032 | 3.81862 | 14.1232 | 20.4905 | 10.3663 | 14.3748 | 8.52547 | −48.5529 | ||||||||||||||||||
1.16 | −3.42061 | −0.613467 | 3.70058 | 3.50938 | 2.09843 | 16.1360 | 14.7066 | −26.6237 | −12.0042 | ||||||||||||||||||
1.17 | −3.41983 | 7.59300 | 3.69524 | 4.48488 | −25.9668 | −4.49298 | 14.7215 | 30.6536 | −15.3375 | ||||||||||||||||||
1.18 | −3.32782 | 9.69808 | 3.07435 | −12.4114 | −32.2734 | 29.0135 | 16.3916 | 67.0527 | 41.3030 | ||||||||||||||||||
1.19 | −3.28242 | 2.93579 | 2.77430 | 18.0532 | −9.63649 | 12.8406 | 17.1530 | −18.3812 | −59.2581 | ||||||||||||||||||
1.20 | −3.05184 | −4.83017 | 1.31373 | −18.6497 | 14.7409 | 8.22006 | 20.4054 | −3.66951 | 56.9157 | ||||||||||||||||||
See all 65 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(547\) | \(-1\) |
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 | 547.4.a.a | ✓ | 65 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
547.4.a.a | ✓ | 65 | 1.a | even | 1 | 1 | trivial |