Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, 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("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(0\) |
Dimension: | \(169\) |
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 | −2.75446 | 1.69224 | 5.58704 | 1.99190 | −4.66119 | −2.92850 | −9.88036 | −0.136337 | −5.48661 | ||||||||||||||||||
1.2 | −2.75254 | −1.96907 | 5.57647 | −0.0473576 | 5.41994 | 2.07710 | −9.84438 | 0.877234 | 0.130354 | ||||||||||||||||||
1.3 | −2.71035 | −1.96664 | 5.34597 | 2.92225 | 5.33028 | 3.98832 | −9.06874 | 0.867686 | −7.92031 | ||||||||||||||||||
1.4 | −2.70848 | 3.38397 | 5.33587 | −0.801714 | −9.16542 | 2.62162 | −9.03513 | 8.45127 | 2.17143 | ||||||||||||||||||
1.5 | −2.70691 | 1.62616 | 5.32735 | −1.60888 | −4.40186 | −2.81542 | −9.00682 | −0.355610 | 4.35510 | ||||||||||||||||||
1.6 | −2.69664 | −0.711836 | 5.27186 | 2.29086 | 1.91957 | 3.32005 | −8.82303 | −2.49329 | −6.17762 | ||||||||||||||||||
1.7 | −2.69608 | 1.22457 | 5.26883 | −1.75306 | −3.30153 | 4.29034 | −8.81301 | −1.50043 | 4.72638 | ||||||||||||||||||
1.8 | −2.66018 | 0.0465626 | 5.07657 | −3.78943 | −0.123865 | 2.50882 | −8.18425 | −2.99783 | 10.0806 | ||||||||||||||||||
1.9 | −2.60952 | −0.136825 | 4.80961 | −0.260304 | 0.357049 | −0.298256 | −7.33174 | −2.98128 | 0.679270 | ||||||||||||||||||
1.10 | −2.60584 | −2.87607 | 4.79042 | −4.02377 | 7.49460 | 0.529095 | −7.27140 | 5.27181 | 10.4853 | ||||||||||||||||||
1.11 | −2.57271 | 0.131094 | 4.61881 | 4.05012 | −0.337267 | −4.42802 | −6.73744 | −2.98281 | −10.4198 | ||||||||||||||||||
1.12 | −2.50053 | 2.23425 | 4.25264 | −3.72100 | −5.58681 | −1.83421 | −5.63280 | 1.99189 | 9.30447 | ||||||||||||||||||
1.13 | −2.48779 | −1.56706 | 4.18912 | −0.470974 | 3.89852 | −0.335999 | −5.44607 | −0.544327 | 1.17169 | ||||||||||||||||||
1.14 | −2.47925 | −2.94109 | 4.14669 | −0.477027 | 7.29170 | −3.55930 | −5.32218 | 5.65002 | 1.18267 | ||||||||||||||||||
1.15 | −2.47225 | −1.54593 | 4.11203 | 3.04029 | 3.82192 | −2.57940 | −5.22147 | −0.610108 | −7.51637 | ||||||||||||||||||
1.16 | −2.43156 | 2.09261 | 3.91247 | 2.37281 | −5.08829 | 3.03145 | −4.65029 | 1.37900 | −5.76963 | ||||||||||||||||||
1.17 | −2.35712 | 0.851105 | 3.55600 | 1.53859 | −2.00615 | 0.407410 | −3.66768 | −2.27562 | −3.62663 | ||||||||||||||||||
1.18 | −2.35439 | −0.664496 | 3.54317 | −2.57609 | 1.56449 | 5.27951 | −3.63324 | −2.55844 | 6.06514 | ||||||||||||||||||
1.19 | −2.32136 | −1.73102 | 3.38869 | −3.82853 | 4.01832 | −3.14873 | −3.22365 | −0.00355516 | 8.88737 | ||||||||||||||||||
1.20 | −2.31715 | 2.98534 | 3.36921 | 4.10060 | −6.91750 | 4.34971 | −3.17266 | 5.91228 | −9.50172 | ||||||||||||||||||
See next 80 embeddings (of 169 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(23\) | \(1\) |
\(349\) | \(-1\) |
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 | 8027.2.a.e | ✓ | 169 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8027.2.a.e | ✓ | 169 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{169} - 6 T_{2}^{168} - 244 T_{2}^{167} + 1522 T_{2}^{166} + 29077 T_{2}^{165} + \cdots - 90567403569152 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8027))\).