Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8019,2,Mod(1,8019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8019, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8019 = 3^{6} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8019.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: | \(64.0320373809\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
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 | −2.78677 | 0 | 5.76607 | 0.0591933 | 0 | 0.765141 | −10.4952 | 0 | −0.164958 | ||||||||||||||||||
1.2 | −2.76227 | 0 | 5.63012 | 1.74188 | 0 | 4.23367 | −10.0274 | 0 | −4.81154 | ||||||||||||||||||
1.3 | −2.74869 | 0 | 5.55528 | −3.20604 | 0 | −4.29093 | −9.77234 | 0 | 8.81241 | ||||||||||||||||||
1.4 | −2.58854 | 0 | 4.70056 | −3.46451 | 0 | 0.848497 | −6.99050 | 0 | 8.96803 | ||||||||||||||||||
1.5 | −2.49176 | 0 | 4.20888 | 3.55698 | 0 | −4.04430 | −5.50400 | 0 | −8.86315 | ||||||||||||||||||
1.6 | −2.48985 | 0 | 4.19936 | −1.09265 | 0 | 2.65687 | −5.47609 | 0 | 2.72053 | ||||||||||||||||||
1.7 | −2.27724 | 0 | 3.18582 | −3.40276 | 0 | 0.928464 | −2.70039 | 0 | 7.74890 | ||||||||||||||||||
1.8 | −2.25095 | 0 | 3.06678 | −2.01161 | 0 | −1.18945 | −2.40127 | 0 | 4.52804 | ||||||||||||||||||
1.9 | −2.16515 | 0 | 2.68787 | 3.05787 | 0 | 3.25666 | −1.48933 | 0 | −6.62075 | ||||||||||||||||||
1.10 | −2.04918 | 0 | 2.19916 | −3.85227 | 0 | 4.47630 | −0.408107 | 0 | 7.89402 | ||||||||||||||||||
1.11 | −1.93884 | 0 | 1.75908 | −0.334950 | 0 | −4.22786 | 0.467097 | 0 | 0.649413 | ||||||||||||||||||
1.12 | −1.81767 | 0 | 1.30394 | 3.09910 | 0 | 0.137252 | 1.26521 | 0 | −5.63316 | ||||||||||||||||||
1.13 | −1.69020 | 0 | 0.856762 | −0.595209 | 0 | 0.410093 | 1.93230 | 0 | 1.00602 | ||||||||||||||||||
1.14 | −1.56489 | 0 | 0.448896 | −4.28242 | 0 | 1.60202 | 2.42731 | 0 | 6.70153 | ||||||||||||||||||
1.15 | −1.53979 | 0 | 0.370949 | 1.28583 | 0 | 3.45759 | 2.50839 | 0 | −1.97991 | ||||||||||||||||||
1.16 | −1.42916 | 0 | 0.0424985 | −0.596655 | 0 | −4.06486 | 2.79758 | 0 | 0.852715 | ||||||||||||||||||
1.17 | −1.23478 | 0 | −0.475321 | 2.26882 | 0 | −3.95112 | 3.05647 | 0 | −2.80149 | ||||||||||||||||||
1.18 | −1.04797 | 0 | −0.901755 | −2.67790 | 0 | 1.71332 | 3.04096 | 0 | 2.80637 | ||||||||||||||||||
1.19 | −0.892531 | 0 | −1.20339 | −2.80076 | 0 | −1.37622 | 2.85912 | 0 | 2.49977 | ||||||||||||||||||
1.20 | −0.724143 | 0 | −1.47562 | 2.15850 | 0 | −0.509330 | 2.51684 | 0 | −1.56306 | ||||||||||||||||||
See all 48 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(1\) |
\(11\) | \(1\) |
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 | 8019.2.a.i | ✓ | 48 |
3.b | odd | 2 | 1 | 8019.2.a.j | yes | 48 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8019.2.a.i | ✓ | 48 | 1.a | even | 1 | 1 | trivial |
8019.2.a.j | yes | 48 | 3.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{48} + 6 T_{2}^{47} - 57 T_{2}^{46} - 400 T_{2}^{45} + 1407 T_{2}^{44} + 12342 T_{2}^{43} + \cdots + 6813 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8019))\).