Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2563,2,Mod(1,2563)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2563, 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("2563.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2563 = 11 \cdot 233 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2563.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: | \(20.4656580381\) |
Analytic rank: | \(0\) |
Dimension: | \(45\) |
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 | −2.70718 | 1.46397 | 5.32882 | 0.250551 | −3.96323 | −0.994047 | −9.01171 | −0.856791 | −0.678287 | ||||||||||||||||||
1.2 | −2.58654 | 2.77304 | 4.69019 | 4.02297 | −7.17259 | −0.351276 | −6.95830 | 4.68977 | −10.4056 | ||||||||||||||||||
1.3 | −2.52909 | −0.770947 | 4.39628 | 3.50476 | 1.94979 | −4.50615 | −6.06041 | −2.40564 | −8.86386 | ||||||||||||||||||
1.4 | −2.34189 | −1.85027 | 3.48444 | −1.38150 | 4.33312 | −0.582255 | −3.47639 | 0.423486 | 3.23532 | ||||||||||||||||||
1.5 | −2.30257 | 0.482027 | 3.30185 | −2.32678 | −1.10990 | −2.51327 | −2.99761 | −2.76765 | 5.35759 | ||||||||||||||||||
1.6 | −1.89466 | 2.99980 | 1.58973 | 2.28311 | −5.68360 | −3.69382 | 0.777328 | 5.99881 | −4.32571 | ||||||||||||||||||
1.7 | −1.82664 | −0.0402198 | 1.33663 | 0.447996 | 0.0734673 | 1.52619 | 1.21174 | −2.99838 | −0.818330 | ||||||||||||||||||
1.8 | −1.79218 | −2.15949 | 1.21192 | −0.344282 | 3.87021 | 2.09531 | 1.41238 | 1.66341 | 0.617016 | ||||||||||||||||||
1.9 | −1.75979 | 3.40508 | 1.09688 | −2.18301 | −5.99224 | −0.895247 | 1.58931 | 8.59457 | 3.84165 | ||||||||||||||||||
1.10 | −1.57507 | 2.56434 | 0.480842 | 3.68930 | −4.03901 | 4.54649 | 2.39278 | 3.57582 | −5.81090 | ||||||||||||||||||
1.11 | −1.44485 | −1.97476 | 0.0875777 | 0.813719 | 2.85322 | −3.62864 | 2.76315 | 0.899659 | −1.17570 | ||||||||||||||||||
1.12 | −1.25993 | −2.65835 | −0.412587 | 4.38316 | 3.34933 | −2.39478 | 3.03968 | 4.06685 | −5.52246 | ||||||||||||||||||
1.13 | −1.23616 | 0.970298 | −0.471908 | 0.266522 | −1.19944 | −1.54832 | 3.05567 | −2.05852 | −0.329464 | ||||||||||||||||||
1.14 | −1.12952 | −2.93696 | −0.724192 | −2.56654 | 3.31735 | 0.444238 | 3.07702 | 5.62575 | 2.89895 | ||||||||||||||||||
1.15 | −1.02056 | −0.462786 | −0.958455 | 1.71072 | 0.472301 | −4.72321 | 3.01928 | −2.78583 | −1.74589 | ||||||||||||||||||
1.16 | −0.957968 | 0.934427 | −1.08230 | 3.06265 | −0.895151 | 1.67167 | 2.95274 | −2.12685 | −2.93392 | ||||||||||||||||||
1.17 | −0.827030 | −1.01201 | −1.31602 | −2.77734 | 0.836966 | 2.14903 | 2.74245 | −1.97583 | 2.29695 | ||||||||||||||||||
1.18 | −0.617158 | 1.85866 | −1.61912 | −2.84817 | −1.14709 | −4.80487 | 2.23357 | 0.454614 | 1.75777 | ||||||||||||||||||
1.19 | −0.0567764 | −1.29238 | −1.99678 | 3.37731 | 0.0733764 | 2.30084 | 0.226923 | −1.32977 | −0.191751 | ||||||||||||||||||
1.20 | 0.0394839 | 0.213929 | −1.99844 | −1.33992 | 0.00844676 | −3.36689 | −0.157874 | −2.95423 | −0.0529053 | ||||||||||||||||||
See all 45 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(11\) | \(1\) |
\(233\) | \(-1\) |
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 | 2563.2.a.j | ✓ | 45 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
2563.2.a.j | ✓ | 45 | 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2563))\):
\( T_{2}^{45} - 12 T_{2}^{44} + 548 T_{2}^{42} - 1579 T_{2}^{41} - 10319 T_{2}^{40} + 51320 T_{2}^{39} + 91836 T_{2}^{38} - 844192 T_{2}^{37} - 99019 T_{2}^{36} + 8784896 T_{2}^{35} - 7305788 T_{2}^{34} - 62516652 T_{2}^{33} + \cdots + 11304 \) |
\( T_{3}^{45} - 5 T_{3}^{44} - 81 T_{3}^{43} + 426 T_{3}^{42} + 2987 T_{3}^{41} - 16680 T_{3}^{40} - 66403 T_{3}^{39} + 398477 T_{3}^{38} + 992611 T_{3}^{37} - 6503200 T_{3}^{36} - 10523931 T_{3}^{35} + 76931054 T_{3}^{34} + \cdots - 8192 \) |