Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8035,2,Mod(1,8035)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8035, 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("8035.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8035 = 5 \cdot 1607 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8035.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: | \(64.1597980241\) |
Analytic rank: | \(0\) |
Dimension: | \(127\) |
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 | −2.73873 | 0.672106 | 5.50064 | −1.00000 | −1.84072 | −4.04942 | −9.58729 | −2.54827 | 2.73873 | ||||||||||||||||||
1.2 | −2.68442 | −1.35317 | 5.20611 | −1.00000 | 3.63248 | −0.554981 | −8.60654 | −1.16892 | 2.68442 | ||||||||||||||||||
1.3 | −2.65256 | 2.52646 | 5.03608 | −1.00000 | −6.70158 | −1.65453 | −8.05337 | 3.38299 | 2.65256 | ||||||||||||||||||
1.4 | −2.61836 | 3.26899 | 4.85584 | −1.00000 | −8.55940 | 1.91983 | −7.47762 | 7.68627 | 2.61836 | ||||||||||||||||||
1.5 | −2.47063 | −2.44892 | 4.10400 | −1.00000 | 6.05037 | 0.863350 | −5.19820 | 2.99721 | 2.47063 | ||||||||||||||||||
1.6 | −2.46463 | −1.44696 | 4.07438 | −1.00000 | 3.56623 | 3.47016 | −5.11258 | −0.906295 | 2.46463 | ||||||||||||||||||
1.7 | −2.44893 | 0.721523 | 3.99726 | −1.00000 | −1.76696 | −0.931483 | −4.89116 | −2.47940 | 2.44893 | ||||||||||||||||||
1.8 | −2.44268 | 2.17434 | 3.96666 | −1.00000 | −5.31121 | 1.92177 | −4.80392 | 1.72777 | 2.44268 | ||||||||||||||||||
1.9 | −2.42672 | −1.34880 | 3.88897 | −1.00000 | 3.27316 | −0.627259 | −4.58399 | −1.18074 | 2.42672 | ||||||||||||||||||
1.10 | −2.38169 | 0.502549 | 3.67242 | −1.00000 | −1.19691 | 1.76739 | −3.98319 | −2.74744 | 2.38169 | ||||||||||||||||||
1.11 | −2.33324 | −1.40461 | 3.44401 | −1.00000 | 3.27730 | −3.84799 | −3.36922 | −1.02706 | 2.33324 | ||||||||||||||||||
1.12 | −2.32831 | 1.94155 | 3.42102 | −1.00000 | −4.52053 | 0.423460 | −3.30857 | 0.769626 | 2.32831 | ||||||||||||||||||
1.13 | −2.25182 | 0.156734 | 3.07069 | −1.00000 | −0.352938 | 4.92465 | −2.41100 | −2.97543 | 2.25182 | ||||||||||||||||||
1.14 | −2.23096 | 0.376155 | 2.97717 | −1.00000 | −0.839185 | −1.46614 | −2.18003 | −2.85851 | 2.23096 | ||||||||||||||||||
1.15 | −2.19837 | −2.82193 | 2.83283 | −1.00000 | 6.20363 | 2.67326 | −1.83086 | 4.96326 | 2.19837 | ||||||||||||||||||
1.16 | −2.17325 | 2.30276 | 2.72303 | −1.00000 | −5.00447 | −1.58489 | −1.57132 | 2.30268 | 2.17325 | ||||||||||||||||||
1.17 | −2.09243 | −1.43223 | 2.37828 | −1.00000 | 2.99685 | −1.24970 | −0.791531 | −0.948714 | 2.09243 | ||||||||||||||||||
1.18 | −2.07647 | −1.16893 | 2.31172 | −1.00000 | 2.42725 | −0.555409 | −0.647270 | −1.63360 | 2.07647 | ||||||||||||||||||
1.19 | −2.04769 | 1.24838 | 2.19303 | −1.00000 | −2.55629 | −4.80946 | −0.395268 | −1.44156 | 2.04769 | ||||||||||||||||||
1.20 | −1.99934 | −2.20170 | 1.99734 | −1.00000 | 4.40194 | 0.230566 | 0.00531235 | 1.84749 | 1.99934 | ||||||||||||||||||
See next 80 embeddings (of 127 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(5\) | \(1\) |
\(1607\) | \(-1\) |
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 | 8035.2.a.c | ✓ | 127 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8035.2.a.c | ✓ | 127 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{127} - 19 T_{2}^{126} - 9 T_{2}^{125} + 2414 T_{2}^{124} - 10468 T_{2}^{123} - 135985 T_{2}^{122} + \cdots - 28908672 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8035))\).