Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2669,2,Mod(1,2669)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2669, 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("2669.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2669 = 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2669.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: | \(21.3120722995\) |
Analytic rank: | \(1\) |
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 | −2.57997 | 2.27677 | 4.65627 | 0.454801 | −5.87400 | −2.24616 | −6.85310 | 2.18367 | −1.17338 | ||||||||||||||||||
1.2 | −2.57201 | 2.33809 | 4.61521 | 0.369809 | −6.01357 | 2.27226 | −6.72634 | 2.46665 | −0.951150 | ||||||||||||||||||
1.3 | −2.52566 | −1.38618 | 4.37894 | 3.81505 | 3.50102 | −1.76068 | −6.00839 | −1.07850 | −9.63552 | ||||||||||||||||||
1.4 | −2.50488 | 0.477138 | 4.27442 | 0.361901 | −1.19517 | −0.370992 | −5.69715 | −2.77234 | −0.906519 | ||||||||||||||||||
1.5 | −2.33974 | −2.03142 | 3.47436 | −3.05646 | 4.75298 | 0.309944 | −3.44962 | 1.12665 | 7.15130 | ||||||||||||||||||
1.6 | −2.29985 | −1.57945 | 3.28932 | −1.13990 | 3.63250 | −3.55948 | −2.96525 | −0.505346 | 2.62159 | ||||||||||||||||||
1.7 | −2.25978 | −3.22925 | 3.10659 | −1.10091 | 7.29738 | 2.65511 | −2.50065 | 7.42805 | 2.48780 | ||||||||||||||||||
1.8 | −1.96618 | 1.61430 | 1.86585 | −2.80677 | −3.17400 | 3.78870 | 0.263762 | −0.394028 | 5.51860 | ||||||||||||||||||
1.9 | −1.83672 | 2.17585 | 1.37355 | −2.57891 | −3.99644 | −3.01876 | 1.15062 | 1.73434 | 4.73675 | ||||||||||||||||||
1.10 | −1.77149 | −2.81155 | 1.13817 | 3.99941 | 4.98063 | −2.62351 | 1.52672 | 4.90481 | −7.08491 | ||||||||||||||||||
1.11 | −1.62128 | −0.288989 | 0.628561 | 2.60755 | 0.468532 | 0.210946 | 2.22349 | −2.91649 | −4.22758 | ||||||||||||||||||
1.12 | −1.52876 | −3.31671 | 0.337100 | −0.791880 | 5.07045 | −3.85375 | 2.54217 | 8.00058 | 1.21059 | ||||||||||||||||||
1.13 | −1.45876 | 1.14095 | 0.127991 | 1.62587 | −1.66437 | −2.45935 | 2.73082 | −1.69823 | −2.37176 | ||||||||||||||||||
1.14 | −1.42791 | 0.606117 | 0.0389142 | 1.41385 | −0.865478 | 1.73370 | 2.80025 | −2.63262 | −2.01884 | ||||||||||||||||||
1.15 | −1.37659 | −2.26906 | −0.104998 | −0.453399 | 3.12356 | 4.69088 | 2.89772 | 2.14862 | 0.624145 | ||||||||||||||||||
1.16 | −0.864732 | 0.578982 | −1.25224 | −4.36543 | −0.500664 | −1.93357 | 2.81231 | −2.66478 | 3.77492 | ||||||||||||||||||
1.17 | −0.810938 | −0.989402 | −1.34238 | −2.55175 | 0.802344 | −1.16091 | 2.71046 | −2.02108 | 2.06931 | ||||||||||||||||||
1.18 | −0.440764 | −0.189246 | −1.80573 | 1.67241 | 0.0834127 | −4.38089 | 1.67743 | −2.96419 | −0.737139 | ||||||||||||||||||
1.19 | −0.356197 | −0.420410 | −1.87312 | 2.53359 | 0.149749 | 3.26999 | 1.37959 | −2.82326 | −0.902455 | ||||||||||||||||||
1.20 | −0.325803 | 2.31804 | −1.89385 | −0.307738 | −0.755226 | −0.806220 | 1.26863 | 2.37332 | 0.100262 | ||||||||||||||||||
See all 45 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(17\) | \(-1\) |
\(157\) | \(-1\) |
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 | 2669.2.a.b | ✓ | 45 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
2669.2.a.b | ✓ | 45 | 1.a | even | 1 | 1 | trivial |