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: | \(0\) |
Dimension: | \(71\) |
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 | −5.33809 | −2.63104 | 20.4952 | 12.8347 | 14.0448 | 22.5520 | −66.7005 | −20.0776 | −68.5130 | ||||||||||||||||||
1.2 | −5.26364 | −3.16796 | 19.7059 | 21.3074 | 16.6750 | −14.9641 | −61.6156 | −16.9640 | −112.154 | ||||||||||||||||||
1.3 | −5.16402 | −8.74896 | 18.6671 | −2.06725 | 45.1798 | −11.4836 | −55.0849 | 49.5444 | 10.6753 | ||||||||||||||||||
1.4 | −5.16082 | 9.40532 | 18.6341 | −10.9794 | −48.5392 | −11.5228 | −54.8805 | 61.4600 | 56.6629 | ||||||||||||||||||
1.5 | −5.04533 | −1.70191 | 17.4553 | 1.56697 | 8.58669 | −17.5256 | −47.7054 | −24.1035 | −7.90590 | ||||||||||||||||||
1.6 | −4.93277 | 2.64687 | 16.3322 | −3.58160 | −13.0564 | 9.94238 | −41.1009 | −19.9941 | 17.6672 | ||||||||||||||||||
1.7 | −4.85758 | 9.04814 | 15.5961 | 16.7670 | −43.9521 | 18.8884 | −36.8987 | 54.8688 | −81.4469 | ||||||||||||||||||
1.8 | −4.68521 | 2.05946 | 13.9512 | 16.8174 | −9.64900 | 3.12603 | −27.8825 | −22.7586 | −78.7929 | ||||||||||||||||||
1.9 | −4.65518 | −5.82218 | 13.6707 | −6.25020 | 27.1033 | −2.07510 | −26.3983 | 6.89779 | 29.0958 | ||||||||||||||||||
1.10 | −4.53918 | −1.35981 | 12.6041 | −14.6057 | 6.17242 | 5.88252 | −20.8990 | −25.1509 | 66.2981 | ||||||||||||||||||
1.11 | −4.13291 | 8.01594 | 9.08096 | −4.43214 | −33.1292 | 17.8969 | −4.46750 | 37.2553 | 18.3177 | ||||||||||||||||||
1.12 | −4.00233 | 4.42663 | 8.01862 | −17.4366 | −17.7168 | −28.8522 | −0.0745319 | −7.40492 | 69.7871 | ||||||||||||||||||
1.13 | −3.65756 | −5.29226 | 5.37772 | 15.7763 | 19.3567 | −21.1834 | 9.59114 | 1.00804 | −57.7027 | ||||||||||||||||||
1.14 | −3.61662 | 5.98739 | 5.07997 | 14.5299 | −21.6541 | 21.3024 | 10.5606 | 8.84881 | −52.5491 | ||||||||||||||||||
1.15 | −3.45260 | −9.18913 | 3.92046 | −10.5912 | 31.7264 | 24.4389 | 14.0850 | 57.4401 | 36.5672 | ||||||||||||||||||
1.16 | −3.19990 | 5.94033 | 2.23933 | −4.08668 | −19.0084 | −18.1886 | 18.4335 | 8.28747 | 13.0769 | ||||||||||||||||||
1.17 | −3.17215 | −0.466644 | 2.06251 | −2.33487 | 1.48026 | −2.84434 | 18.8346 | −26.7822 | 7.40655 | ||||||||||||||||||
1.18 | −3.00219 | −8.77445 | 1.01316 | −10.0921 | 26.3426 | −3.02021 | 20.9758 | 49.9910 | 30.2985 | ||||||||||||||||||
1.19 | −2.54195 | 10.1442 | −1.53851 | 19.6797 | −25.7861 | −26.4188 | 24.2464 | 75.9054 | −50.0248 | ||||||||||||||||||
1.20 | −2.30656 | 0.950194 | −2.67977 | −5.29729 | −2.19168 | 32.9235 | 24.6336 | −26.0971 | 12.2185 | ||||||||||||||||||
See all 71 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.b | ✓ | 71 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
547.4.a.b | ✓ | 71 | 1.a | even | 1 | 1 | trivial |