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: | \(22\) |
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 | −2.65075 | −1.00000 | 5.02646 | 2.28366 | 2.65075 | 3.33771 | −8.02237 | 1.00000 | −6.05341 | ||||||||||||||||||
1.2 | −2.17605 | −1.00000 | 2.73521 | 1.58006 | 2.17605 | −0.969003 | −1.59985 | 1.00000 | −3.43828 | ||||||||||||||||||
1.3 | −2.12762 | −1.00000 | 2.52678 | −3.72932 | 2.12762 | −2.25712 | −1.12080 | 1.00000 | 7.93460 | ||||||||||||||||||
1.4 | −1.99316 | −1.00000 | 1.97270 | −1.27823 | 1.99316 | 0.558075 | 0.0544076 | 1.00000 | 2.54772 | ||||||||||||||||||
1.5 | −1.52080 | −1.00000 | 0.312840 | 4.21021 | 1.52080 | −4.25725 | 2.56584 | 1.00000 | −6.40289 | ||||||||||||||||||
1.6 | −1.32697 | −1.00000 | −0.239163 | −0.116261 | 1.32697 | 0.614865 | 2.97129 | 1.00000 | 0.154274 | ||||||||||||||||||
1.7 | −1.06401 | −1.00000 | −0.867885 | 2.98305 | 1.06401 | −1.35946 | 3.05146 | 1.00000 | −3.17400 | ||||||||||||||||||
1.8 | −1.04848 | −1.00000 | −0.900691 | −0.0290827 | 1.04848 | 2.65326 | 3.04131 | 1.00000 | 0.0304926 | ||||||||||||||||||
1.9 | −0.770110 | −1.00000 | −1.40693 | −2.32965 | 0.770110 | −2.53396 | 2.62371 | 1.00000 | 1.79409 | ||||||||||||||||||
1.10 | −0.193122 | −1.00000 | −1.96270 | 0.930576 | 0.193122 | 3.24035 | 0.765286 | 1.00000 | −0.179715 | ||||||||||||||||||
1.11 | −0.0913921 | −1.00000 | −1.99165 | −1.96751 | 0.0913921 | −3.33061 | 0.364805 | 1.00000 | 0.179815 | ||||||||||||||||||
1.12 | 0.241023 | −1.00000 | −1.94191 | −3.77754 | −0.241023 | 3.81286 | −0.950090 | 1.00000 | −0.910473 | ||||||||||||||||||
1.13 | 0.321205 | −1.00000 | −1.89683 | 2.50638 | −0.321205 | 1.79876 | −1.25168 | 1.00000 | 0.805062 | ||||||||||||||||||
1.14 | 0.977627 | −1.00000 | −1.04425 | 4.02352 | −0.977627 | 0.138355 | −2.97614 | 1.00000 | 3.93350 | ||||||||||||||||||
1.15 | 1.13663 | −1.00000 | −0.708075 | 0.214323 | −1.13663 | −3.67011 | −3.07808 | 1.00000 | 0.243606 | ||||||||||||||||||
1.16 | 1.23345 | −1.00000 | −0.478591 | 1.09712 | −1.23345 | 2.41639 | −3.05723 | 1.00000 | 1.35325 | ||||||||||||||||||
1.17 | 1.71068 | −1.00000 | 0.926413 | −0.235086 | −1.71068 | −1.75585 | −1.83656 | 1.00000 | −0.402156 | ||||||||||||||||||
1.18 | 2.05356 | −1.00000 | 2.21711 | 2.39106 | −2.05356 | −1.51026 | 0.445844 | 1.00000 | 4.91018 | ||||||||||||||||||
1.19 | 2.08589 | −1.00000 | 2.35095 | 0.140268 | −2.08589 | 1.76887 | 0.732041 | 1.00000 | 0.292585 | ||||||||||||||||||
1.20 | 2.23779 | −1.00000 | 3.00772 | −1.81110 | −2.23779 | 1.95143 | 2.25507 | 1.00000 | −4.05288 | ||||||||||||||||||
See all 22 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.g | ✓ | 22 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
4029.2.a.g | ✓ | 22 | 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4029))\):
\( T_{2}^{22} - 2 T_{2}^{21} - 28 T_{2}^{20} + 54 T_{2}^{19} + 332 T_{2}^{18} - 609 T_{2}^{17} - 2187 T_{2}^{16} + \cdots - 8 \) |
\( T_{5}^{22} - 5 T_{5}^{21} - 47 T_{5}^{20} + 261 T_{5}^{19} + 798 T_{5}^{18} - 5416 T_{5}^{17} + \cdots + 15 \) |