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: | \(44\) |
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 | −2.66435 | −1.21779 | 5.09874 | 3.39301 | 3.24461 | 0.452289 | −8.25611 | −1.51699 | −9.04015 | ||||||||||||||||||
1.2 | −2.58466 | −0.193713 | 4.68045 | −3.10936 | 0.500683 | −2.15080 | −6.92806 | −2.96248 | 8.03663 | ||||||||||||||||||
1.3 | −2.47158 | −0.563298 | 4.10869 | 0.986024 | 1.39224 | 1.84052 | −5.21180 | −2.68269 | −2.43703 | ||||||||||||||||||
1.4 | −2.24601 | 2.56768 | 3.04457 | −0.863410 | −5.76704 | −1.60230 | −2.34612 | 3.59297 | 1.93923 | ||||||||||||||||||
1.5 | −2.22384 | 0.314537 | 2.94545 | 0.0859647 | −0.699480 | 3.34563 | −2.10253 | −2.90107 | −0.191171 | ||||||||||||||||||
1.6 | −2.20697 | −2.55903 | 2.87071 | 0.548326 | 5.64771 | −0.683538 | −1.92162 | 3.54866 | −1.21014 | ||||||||||||||||||
1.7 | −2.10891 | 1.58356 | 2.44749 | 3.64832 | −3.33958 | 1.15549 | −0.943725 | −0.492342 | −7.69398 | ||||||||||||||||||
1.8 | −1.92756 | 2.09351 | 1.71550 | 2.15978 | −4.03537 | −4.43260 | 0.548399 | 1.38277 | −4.16311 | ||||||||||||||||||
1.9 | −1.79880 | −1.32633 | 1.23567 | −1.96485 | 2.38580 | −4.92295 | 1.37488 | −1.24084 | 3.53437 | ||||||||||||||||||
1.10 | −1.53889 | 1.10780 | 0.368195 | −0.710380 | −1.70479 | 3.64463 | 2.51117 | −1.77278 | 1.09320 | ||||||||||||||||||
1.11 | −1.51494 | −2.79513 | 0.295043 | −4.15377 | 4.23445 | 2.06066 | 2.58291 | 4.81275 | 6.29271 | ||||||||||||||||||
1.12 | −1.51197 | −1.16260 | 0.286045 | −1.11918 | 1.75782 | 0.899408 | 2.59144 | −1.64835 | 1.69216 | ||||||||||||||||||
1.13 | −1.41614 | 2.89956 | 0.00545620 | −3.69241 | −4.10619 | 1.88343 | 2.82456 | 5.40747 | 5.22898 | ||||||||||||||||||
1.14 | −1.21570 | −1.96904 | −0.522083 | 1.79237 | 2.39375 | 0.810694 | 3.06609 | 0.877101 | −2.17897 | ||||||||||||||||||
1.15 | −1.16247 | −2.99037 | −0.648659 | 1.53773 | 3.47622 | 4.73309 | 3.07899 | 5.94228 | −1.78757 | ||||||||||||||||||
1.16 | −0.796888 | 0.740012 | −1.36497 | 3.76063 | −0.589706 | −1.84006 | 2.68150 | −2.45238 | −2.99680 | ||||||||||||||||||
1.17 | −0.786416 | −1.22702 | −1.38155 | −3.42260 | 0.964949 | −1.13473 | 2.65930 | −1.49442 | 2.69159 | ||||||||||||||||||
1.18 | −0.773581 | 1.40975 | −1.40157 | 0.934109 | −1.09056 | 1.77239 | 2.63139 | −1.01259 | −0.722609 | ||||||||||||||||||
1.19 | −0.767913 | 3.21536 | −1.41031 | −0.0813250 | −2.46911 | −1.52019 | 2.61882 | 7.33853 | 0.0624505 | ||||||||||||||||||
1.20 | −0.538936 | −3.19875 | −1.70955 | 3.08173 | 1.72392 | 0.0973693 | 1.99921 | 7.23202 | −1.66085 | ||||||||||||||||||
See all 44 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.a | ✓ | 44 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
2669.2.a.a | ✓ | 44 | 1.a | even | 1 | 1 | trivial |