Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(1\) |
Dimension: | \(35\) |
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 | −1.00000 | −3.27997 | 1.00000 | 2.11941 | 3.27997 | −0.124927 | −1.00000 | 7.75819 | −2.11941 | ||||||||||||||||||
1.2 | −1.00000 | −3.25702 | 1.00000 | −1.18968 | 3.25702 | 1.65832 | −1.00000 | 7.60820 | 1.18968 | ||||||||||||||||||
1.3 | −1.00000 | −2.93683 | 1.00000 | 0.0231797 | 2.93683 | −4.16598 | −1.00000 | 5.62497 | −0.0231797 | ||||||||||||||||||
1.4 | −1.00000 | −2.83579 | 1.00000 | 4.39396 | 2.83579 | −1.33504 | −1.00000 | 5.04172 | −4.39396 | ||||||||||||||||||
1.5 | −1.00000 | −2.39986 | 1.00000 | −1.11547 | 2.39986 | 2.17590 | −1.00000 | 2.75933 | 1.11547 | ||||||||||||||||||
1.6 | −1.00000 | −2.23091 | 1.00000 | 1.94904 | 2.23091 | 1.55699 | −1.00000 | 1.97697 | −1.94904 | ||||||||||||||||||
1.7 | −1.00000 | −2.01951 | 1.00000 | 3.52220 | 2.01951 | −0.0194784 | −1.00000 | 1.07840 | −3.52220 | ||||||||||||||||||
1.8 | −1.00000 | −1.96432 | 1.00000 | −0.678471 | 1.96432 | 4.37365 | −1.00000 | 0.858567 | 0.678471 | ||||||||||||||||||
1.9 | −1.00000 | −1.95232 | 1.00000 | −1.60299 | 1.95232 | −2.46247 | −1.00000 | 0.811553 | 1.60299 | ||||||||||||||||||
1.10 | −1.00000 | −1.90524 | 1.00000 | −3.49980 | 1.90524 | −2.88392 | −1.00000 | 0.629935 | 3.49980 | ||||||||||||||||||
1.11 | −1.00000 | −1.74374 | 1.00000 | −3.34943 | 1.74374 | 0.122108 | −1.00000 | 0.0406325 | 3.34943 | ||||||||||||||||||
1.12 | −1.00000 | −1.52925 | 1.00000 | 3.51675 | 1.52925 | −1.62140 | −1.00000 | −0.661396 | −3.51675 | ||||||||||||||||||
1.13 | −1.00000 | −1.35256 | 1.00000 | −0.395568 | 1.35256 | 1.50560 | −1.00000 | −1.17057 | 0.395568 | ||||||||||||||||||
1.14 | −1.00000 | −1.19422 | 1.00000 | 1.77357 | 1.19422 | 2.63831 | −1.00000 | −1.57384 | −1.77357 | ||||||||||||||||||
1.15 | −1.00000 | −0.841269 | 1.00000 | −1.88225 | 0.841269 | −4.21612 | −1.00000 | −2.29227 | 1.88225 | ||||||||||||||||||
1.16 | −1.00000 | −0.715791 | 1.00000 | 2.28149 | 0.715791 | −4.66835 | −1.00000 | −2.48764 | −2.28149 | ||||||||||||||||||
1.17 | −1.00000 | −0.237603 | 1.00000 | 3.33211 | 0.237603 | 4.34322 | −1.00000 | −2.94355 | −3.33211 | ||||||||||||||||||
1.18 | −1.00000 | 0.00791248 | 1.00000 | −2.05271 | −0.00791248 | −2.16347 | −1.00000 | −2.99994 | 2.05271 | ||||||||||||||||||
1.19 | −1.00000 | 0.0555653 | 1.00000 | 0.675723 | −0.0555653 | −0.0958620 | −1.00000 | −2.99691 | −0.675723 | ||||||||||||||||||
1.20 | −1.00000 | 0.280261 | 1.00000 | 0.751535 | −0.280261 | 1.30988 | −1.00000 | −2.92145 | −0.751535 | ||||||||||||||||||
See all 35 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
\(2017\) | \(1\) |
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 | 4034.2.a.b | ✓ | 35 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
4034.2.a.b | ✓ | 35 | 1.a | even | 1 | 1 | trivial |