Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(17,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([11, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.bd (of order \(18\), degree \(6\), not minimal) |
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: | no |
Analytic conductor: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 189) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
$q$-expansion
The algebraic \(q\)-expansion of this newform has not been computed, 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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
17.1 | −2.50283 | + | 0.441316i | 0 | 4.19001 | − | 1.52504i | 0.437341 | − | 0.159179i | 0 | −1.48170 | + | 2.19193i | −5.41196 | + | 3.12460i | 0 | −1.02434 | + | 0.591403i | ||||||
17.2 | −2.45739 | + | 0.433304i | 0 | 3.97163 | − | 1.44555i | 0.335948 | − | 0.122275i | 0 | 0.0666399 | − | 2.64491i | −4.81149 | + | 2.77792i | 0 | −0.772573 | + | 0.446045i | ||||||
17.3 | −2.22112 | + | 0.391643i | 0 | 2.90060 | − | 1.05573i | 3.20807 | − | 1.16764i | 0 | −2.62457 | − | 0.334082i | −2.12267 | + | 1.22552i | 0 | −6.66821 | + | 3.84989i | ||||||
17.4 | −1.87320 | + | 0.330296i | 0 | 1.52040 | − | 0.553380i | 0.848304 | − | 0.308757i | 0 | 2.48993 | + | 0.894564i | 0.629295 | − | 0.363324i | 0 | −1.48706 | + | 0.858555i | ||||||
17.5 | −1.66985 | + | 0.294440i | 0 | 0.822331 | − | 0.299304i | −1.39543 | + | 0.507895i | 0 | −0.356869 | − | 2.62157i | 1.65184 | − | 0.953692i | 0 | 2.18062 | − | 1.25898i | ||||||
17.6 | −1.65422 | + | 0.291684i | 0 | 0.771989 | − | 0.280981i | −3.52188 | + | 1.28186i | 0 | −2.17331 | + | 1.50888i | 1.71431 | − | 0.989760i | 0 | 5.45209 | − | 3.14776i | ||||||
17.7 | −1.10401 | + | 0.194666i | 0 | −0.698446 | + | 0.254214i | 3.85196 | − | 1.40200i | 0 | 2.61259 | − | 0.417595i | 2.66330 | − | 1.53766i | 0 | −3.97967 | + | 2.29767i | ||||||
17.8 | −0.892534 | + | 0.157378i | 0 | −1.10754 | + | 0.403110i | 1.14226 | − | 0.415747i | 0 | −1.98483 | + | 1.74942i | 2.49483 | − | 1.44039i | 0 | −0.954073 | + | 0.550834i | ||||||
17.9 | −0.882178 | + | 0.155552i | 0 | −1.12534 | + | 0.409592i | −0.123522 | + | 0.0449584i | 0 | 1.69913 | + | 2.02805i | 2.48059 | − | 1.43217i | 0 | 0.101975 | − | 0.0588754i | ||||||
17.10 | −0.245063 | + | 0.0432112i | 0 | −1.82120 | + | 0.662861i | −1.99870 | + | 0.727467i | 0 | 0.302346 | − | 2.62842i | 0.848674 | − | 0.489982i | 0 | 0.458373 | − | 0.264642i | ||||||
17.11 | −0.0159182 | + | 0.00280680i | 0 | −1.87914 | + | 0.683951i | −3.75147 | + | 1.36542i | 0 | 0.157938 | + | 2.64103i | 0.0559891 | − | 0.0323253i | 0 | 0.0558840 | − | 0.0322646i | ||||||
17.12 | 0.0147002 | − | 0.00259205i | 0 | −1.87918 | + | 0.683964i | −1.54651 | + | 0.562885i | 0 | 2.21011 | − | 1.45445i | −0.0517058 | + | 0.0298524i | 0 | −0.0212751 | + | 0.0122832i | ||||||
17.13 | 0.313923 | − | 0.0553531i | 0 | −1.78390 | + | 0.649287i | 2.68563 | − | 0.977491i | 0 | −2.48320 | − | 0.913082i | −1.07619 | + | 0.621337i | 0 | 0.788975 | − | 0.455515i | ||||||
17.14 | 0.877614 | − | 0.154747i | 0 | −1.13313 | + | 0.412424i | 1.30288 | − | 0.474210i | 0 | 1.81190 | + | 1.92796i | −2.47415 | + | 1.42845i | 0 | 1.07004 | − | 0.617790i | ||||||
17.15 | 0.910598 | − | 0.160563i | 0 | −1.07598 | + | 0.391623i | 0.473927 | − | 0.172495i | 0 | −2.46079 | − | 0.971863i | −2.51844 | + | 1.45402i | 0 | 0.403861 | − | 0.233169i | ||||||
17.16 | 1.38665 | − | 0.244504i | 0 | −0.0163608 | + | 0.00595485i | −1.98299 | + | 0.721749i | 0 | −2.18605 | − | 1.49037i | −2.46004 | + | 1.42030i | 0 | −2.57325 | + | 1.48566i | ||||||
17.17 | 1.57155 | − | 0.277106i | 0 | 0.513586 | − | 0.186930i | −1.78318 | + | 0.649025i | 0 | −1.28547 | + | 2.31248i | −2.00866 | + | 1.15970i | 0 | −2.62250 | + | 1.51410i | ||||||
17.18 | 1.63190 | − | 0.287749i | 0 | 0.700923 | − | 0.255115i | 3.60525 | − | 1.31220i | 0 | 2.03118 | − | 1.69538i | −1.79971 | + | 1.03907i | 0 | 5.50583 | − | 3.17879i | ||||||
17.19 | 2.06025 | − | 0.363278i | 0 | 2.23328 | − | 0.812849i | −0.338534 | + | 0.123216i | 0 | 1.84499 | − | 1.89632i | 0.682329 | − | 0.393943i | 0 | −0.652704 | + | 0.376839i | ||||||
17.20 | 2.26715 | − | 0.399760i | 0 | 3.10078 | − | 1.12859i | 1.73217 | − | 0.630457i | 0 | 0.678971 | + | 2.55715i | 2.59137 | − | 1.49613i | 0 | 3.67505 | − | 2.12179i | ||||||
See next 80 embeddings (of 132 total) |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
189.bd | even | 18 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 567.2.bd.a | 132 | |
3.b | odd | 2 | 1 | 189.2.bd.a | yes | 132 | |
7.d | odd | 6 | 1 | 567.2.ba.a | 132 | ||
21.g | even | 6 | 1 | 189.2.ba.a | ✓ | 132 | |
27.e | even | 9 | 1 | 189.2.ba.a | ✓ | 132 | |
27.f | odd | 18 | 1 | 567.2.ba.a | 132 | ||
189.z | odd | 18 | 1 | 189.2.bd.a | yes | 132 | |
189.bd | even | 18 | 1 | inner | 567.2.bd.a | 132 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
189.2.ba.a | ✓ | 132 | 21.g | even | 6 | 1 | |
189.2.ba.a | ✓ | 132 | 27.e | even | 9 | 1 | |
189.2.bd.a | yes | 132 | 3.b | odd | 2 | 1 | |
189.2.bd.a | yes | 132 | 189.z | odd | 18 | 1 | |
567.2.ba.a | 132 | 7.d | odd | 6 | 1 | ||
567.2.ba.a | 132 | 27.f | odd | 18 | 1 | ||
567.2.bd.a | 132 | 1.a | even | 1 | 1 | trivial | |
567.2.bd.a | 132 | 189.bd | even | 18 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(567, [\chi])\).