Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(0\) |
Dimension: | \(41\) |
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 | −3.33099 | 1.00000 | −3.73356 | −3.33099 | 2.28084 | 1.00000 | 8.09549 | −3.73356 | ||||||||||||||||||
1.2 | 1.00000 | −3.25480 | 1.00000 | 3.43025 | −3.25480 | 2.34297 | 1.00000 | 7.59373 | 3.43025 | ||||||||||||||||||
1.3 | 1.00000 | −3.22313 | 1.00000 | −0.601968 | −3.22313 | −4.66050 | 1.00000 | 7.38856 | −0.601968 | ||||||||||||||||||
1.4 | 1.00000 | −3.13493 | 1.00000 | 2.02213 | −3.13493 | −2.34132 | 1.00000 | 6.82778 | 2.02213 | ||||||||||||||||||
1.5 | 1.00000 | −2.99315 | 1.00000 | −2.87948 | −2.99315 | −2.15668 | 1.00000 | 5.95893 | −2.87948 | ||||||||||||||||||
1.6 | 1.00000 | −2.68141 | 1.00000 | 3.69693 | −2.68141 | 1.66171 | 1.00000 | 4.18994 | 3.69693 | ||||||||||||||||||
1.7 | 1.00000 | −2.35219 | 1.00000 | 0.827343 | −2.35219 | 0.166684 | 1.00000 | 2.53280 | 0.827343 | ||||||||||||||||||
1.8 | 1.00000 | −2.27206 | 1.00000 | 0.0411842 | −2.27206 | 3.26699 | 1.00000 | 2.16224 | 0.0411842 | ||||||||||||||||||
1.9 | 1.00000 | −2.27011 | 1.00000 | −1.81074 | −2.27011 | 2.75406 | 1.00000 | 2.15338 | −1.81074 | ||||||||||||||||||
1.10 | 1.00000 | −2.01222 | 1.00000 | −2.36434 | −2.01222 | 3.66472 | 1.00000 | 1.04902 | −2.36434 | ||||||||||||||||||
1.11 | 1.00000 | −1.56181 | 1.00000 | 1.51273 | −1.56181 | 2.72551 | 1.00000 | −0.560757 | 1.51273 | ||||||||||||||||||
1.12 | 1.00000 | −1.30065 | 1.00000 | 2.66833 | −1.30065 | −4.20545 | 1.00000 | −1.30832 | 2.66833 | ||||||||||||||||||
1.13 | 1.00000 | −1.27958 | 1.00000 | 2.95127 | −1.27958 | 4.74723 | 1.00000 | −1.36266 | 2.95127 | ||||||||||||||||||
1.14 | 1.00000 | −1.08669 | 1.00000 | −0.588357 | −1.08669 | −3.89024 | 1.00000 | −1.81911 | −0.588357 | ||||||||||||||||||
1.15 | 1.00000 | −0.990574 | 1.00000 | 4.23904 | −0.990574 | −4.18696 | 1.00000 | −2.01876 | 4.23904 | ||||||||||||||||||
1.16 | 1.00000 | −0.830898 | 1.00000 | −1.41489 | −0.830898 | −0.234026 | 1.00000 | −2.30961 | −1.41489 | ||||||||||||||||||
1.17 | 1.00000 | −0.425330 | 1.00000 | 2.71720 | −0.425330 | −0.709481 | 1.00000 | −2.81909 | 2.71720 | ||||||||||||||||||
1.18 | 1.00000 | −0.356133 | 1.00000 | 3.98743 | −0.356133 | 1.62862 | 1.00000 | −2.87317 | 3.98743 | ||||||||||||||||||
1.19 | 1.00000 | −0.352298 | 1.00000 | −1.51534 | −0.352298 | −1.04103 | 1.00000 | −2.87589 | −1.51534 | ||||||||||||||||||
1.20 | 1.00000 | −0.148340 | 1.00000 | −1.78404 | −0.148340 | −0.469198 | 1.00000 | −2.97800 | −1.78404 | ||||||||||||||||||
See all 41 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(-1\) |
\(23\) | \(-1\) |
\(131\) | \(-1\) |
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 | 6026.2.a.m | ✓ | 41 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6026.2.a.m | ✓ | 41 | 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):
\( T_{3}^{41} - 4 T_{3}^{40} - 85 T_{3}^{39} + 351 T_{3}^{38} + 3269 T_{3}^{37} - 14026 T_{3}^{36} + \cdots + 13312 \) |
\( T_{5}^{41} - 9 T_{5}^{40} - 100 T_{5}^{39} + 1104 T_{5}^{38} + 3981 T_{5}^{37} - 61305 T_{5}^{36} + \cdots + 1803859328 \) |