Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | no (minimal twist has level 239) |
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 | −5.58089 | 0 | 23.1463 | 10.0408 | 0 | 25.4163 | −84.5299 | 0 | −56.0363 | ||||||||||||||||||
1.2 | −5.29599 | 0 | 20.0475 | −6.13814 | 0 | −8.89768 | −63.8037 | 0 | 32.5075 | ||||||||||||||||||
1.3 | −5.11871 | 0 | 18.2012 | −0.668880 | 0 | 7.37421 | −52.2167 | 0 | 3.42380 | ||||||||||||||||||
1.4 | −4.90101 | 0 | 16.0199 | −18.8248 | 0 | −10.8883 | −39.3055 | 0 | 92.2607 | ||||||||||||||||||
1.5 | −4.79841 | 0 | 15.0248 | 14.4400 | 0 | 1.92684 | −33.7078 | 0 | −69.2892 | ||||||||||||||||||
1.6 | −4.53815 | 0 | 12.5948 | −19.7043 | 0 | 34.6627 | −20.8518 | 0 | 89.4211 | ||||||||||||||||||
1.7 | −4.41344 | 0 | 11.4784 | −16.6195 | 0 | −34.6158 | −15.3518 | 0 | 73.3492 | ||||||||||||||||||
1.8 | −3.91247 | 0 | 7.30741 | 2.39092 | 0 | 22.0359 | 2.70973 | 0 | −9.35442 | ||||||||||||||||||
1.9 | −3.84652 | 0 | 6.79575 | −10.3358 | 0 | 2.00272 | 4.63218 | 0 | 39.7568 | ||||||||||||||||||
1.10 | −3.37030 | 0 | 3.35895 | 1.43026 | 0 | 27.2799 | 15.6418 | 0 | −4.82040 | ||||||||||||||||||
1.11 | −2.83758 | 0 | 0.0518438 | 9.05330 | 0 | −30.7893 | 22.5535 | 0 | −25.6894 | ||||||||||||||||||
1.12 | −2.73040 | 0 | −0.544930 | −10.5995 | 0 | 15.6616 | 23.3311 | 0 | 28.9408 | ||||||||||||||||||
1.13 | −2.40786 | 0 | −2.20221 | 19.1943 | 0 | 10.9735 | 24.5655 | 0 | −46.2171 | ||||||||||||||||||
1.14 | −1.50491 | 0 | −5.73525 | −18.0796 | 0 | −23.9080 | 20.6703 | 0 | 27.2082 | ||||||||||||||||||
1.15 | −1.28174 | 0 | −6.35714 | −12.7359 | 0 | 11.6522 | 18.4021 | 0 | 16.3241 | ||||||||||||||||||
1.16 | −1.09413 | 0 | −6.80288 | 10.8819 | 0 | 4.64141 | 16.1963 | 0 | −11.9062 | ||||||||||||||||||
1.17 | −0.918355 | 0 | −7.15662 | −19.7054 | 0 | 10.7153 | 13.9192 | 0 | 18.0965 | ||||||||||||||||||
1.18 | −0.412743 | 0 | −7.82964 | 15.2997 | 0 | 4.25811 | 6.53358 | 0 | −6.31484 | ||||||||||||||||||
1.19 | −0.271729 | 0 | −7.92616 | 11.3325 | 0 | −27.2237 | 4.32760 | 0 | −3.07937 | ||||||||||||||||||
1.20 | −0.123948 | 0 | −7.98464 | −3.85596 | 0 | −18.4037 | 1.98126 | 0 | 0.477937 | ||||||||||||||||||
See all 37 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(-1\) |
\(239\) | \(-1\) |
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 | 2151.4.a.f | 37 | |
3.b | odd | 2 | 1 | 239.4.a.b | ✓ | 37 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
239.4.a.b | ✓ | 37 | 3.b | odd | 2 | 1 | |
2151.4.a.f | 37 | 1.a | even | 1 | 1 | trivial |