Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
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 | −2.72160 | 1.00000 | 5.40711 | −2.75991 | −2.72160 | 0.631996 | −9.27279 | 1.00000 | 7.51137 | ||||||||||||||||||
1.2 | −2.56536 | 1.00000 | 4.58108 | 2.03955 | −2.56536 | 3.97532 | −6.62141 | 1.00000 | −5.23220 | ||||||||||||||||||
1.3 | −2.38168 | 1.00000 | 3.67240 | 4.36966 | −2.38168 | −4.18483 | −3.98313 | 1.00000 | −10.4071 | ||||||||||||||||||
1.4 | −2.32685 | 1.00000 | 3.41424 | −3.48051 | −2.32685 | 3.88205 | −3.29073 | 1.00000 | 8.09862 | ||||||||||||||||||
1.5 | −2.14934 | 1.00000 | 2.61967 | −2.01369 | −2.14934 | −1.06654 | −1.33187 | 1.00000 | 4.32810 | ||||||||||||||||||
1.6 | −2.03763 | 1.00000 | 2.15194 | 1.97362 | −2.03763 | 1.01571 | −0.309598 | 1.00000 | −4.02151 | ||||||||||||||||||
1.7 | −2.01259 | 1.00000 | 2.05052 | −0.898800 | −2.01259 | −4.86016 | −0.101684 | 1.00000 | 1.80892 | ||||||||||||||||||
1.8 | −1.64354 | 1.00000 | 0.701226 | −1.87389 | −1.64354 | 4.02619 | 2.13459 | 1.00000 | 3.07982 | ||||||||||||||||||
1.9 | −1.29135 | 1.00000 | −0.332415 | 2.00535 | −1.29135 | −2.01131 | 3.01196 | 1.00000 | −2.58960 | ||||||||||||||||||
1.10 | −1.16862 | 1.00000 | −0.634325 | −0.405562 | −1.16862 | −1.60950 | 3.07853 | 1.00000 | 0.473948 | ||||||||||||||||||
1.11 | −0.743888 | 1.00000 | −1.44663 | 0.602376 | −0.743888 | 4.42261 | 2.56391 | 1.00000 | −0.448100 | ||||||||||||||||||
1.12 | −0.691575 | 1.00000 | −1.52172 | 1.10999 | −0.691575 | −0.538181 | 2.43554 | 1.00000 | −0.767639 | ||||||||||||||||||
1.13 | −0.319374 | 1.00000 | −1.89800 | −2.81066 | −0.319374 | −2.62902 | 1.24492 | 1.00000 | 0.897652 | ||||||||||||||||||
1.14 | −0.107521 | 1.00000 | −1.98844 | −4.11054 | −0.107521 | −2.41834 | 0.428841 | 1.00000 | 0.441969 | ||||||||||||||||||
1.15 | 0.0993996 | 1.00000 | −1.99012 | 1.12985 | 0.0993996 | 0.411227 | −0.396616 | 1.00000 | 0.112306 | ||||||||||||||||||
1.16 | 0.384561 | 1.00000 | −1.85211 | −1.18123 | 0.384561 | 2.30830 | −1.48137 | 1.00000 | −0.454254 | ||||||||||||||||||
1.17 | 0.785597 | 1.00000 | −1.38284 | −0.680986 | 0.785597 | 0.961909 | −2.65755 | 1.00000 | −0.534981 | ||||||||||||||||||
1.18 | 1.22160 | 1.00000 | −0.507691 | −3.76998 | 1.22160 | 4.22641 | −3.06340 | 1.00000 | −4.60542 | ||||||||||||||||||
1.19 | 1.36573 | 1.00000 | −0.134771 | 0.714593 | 1.36573 | −2.88499 | −2.91553 | 1.00000 | 0.975944 | ||||||||||||||||||
1.20 | 1.40291 | 1.00000 | −0.0318502 | 3.36351 | 1.40291 | −1.96099 | −2.85050 | 1.00000 | 4.71869 | ||||||||||||||||||
See all 25 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(-1\) |
\(17\) | \(1\) |
\(79\) | \(-1\) |
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 | 4029.2.a.h | ✓ | 25 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
4029.2.a.h | ✓ | 25 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4029))\):
\( T_{2}^{25} + 7 T_{2}^{24} - 11 T_{2}^{23} - 175 T_{2}^{22} - 107 T_{2}^{21} + 1835 T_{2}^{20} + \cdots - 30 \) |
\( T_{5}^{25} + 12 T_{5}^{24} - 526 T_{5}^{22} - 1532 T_{5}^{21} + 7916 T_{5}^{20} + 38952 T_{5}^{19} + \cdots - 670191 \) |