Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,4,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2001.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(118.062821921\) |
Analytic rank: | \(1\) |
Dimension: | \(31\) |
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 | −5.54277 | 3.00000 | 22.7223 | 9.48245 | −16.6283 | −7.42459 | −81.6022 | 9.00000 | −52.5591 | ||||||||||||||||||
1.2 | −4.89797 | 3.00000 | 15.9902 | −7.63127 | −14.6939 | 26.7143 | −39.1355 | 9.00000 | 37.3778 | ||||||||||||||||||
1.3 | −4.77986 | 3.00000 | 14.8471 | 6.64522 | −14.3396 | 17.3119 | −32.7283 | 9.00000 | −31.7633 | ||||||||||||||||||
1.4 | −4.75649 | 3.00000 | 14.6242 | −4.17105 | −14.2695 | −30.3756 | −31.5078 | 9.00000 | 19.8395 | ||||||||||||||||||
1.5 | −4.48602 | 3.00000 | 12.1244 | −19.6077 | −13.4581 | −5.45707 | −18.5020 | 9.00000 | 87.9603 | ||||||||||||||||||
1.6 | −3.66126 | 3.00000 | 5.40480 | −8.70181 | −10.9838 | 1.57002 | 9.50170 | 9.00000 | 31.8596 | ||||||||||||||||||
1.7 | −3.56041 | 3.00000 | 4.67651 | 4.74657 | −10.6812 | 4.84926 | 11.8330 | 9.00000 | −16.8997 | ||||||||||||||||||
1.8 | −3.36157 | 3.00000 | 3.30018 | 17.6011 | −10.0847 | 3.08404 | 15.7988 | 9.00000 | −59.1674 | ||||||||||||||||||
1.9 | −3.23146 | 3.00000 | 2.44236 | −12.0697 | −9.69439 | 18.2309 | 17.9593 | 9.00000 | 39.0029 | ||||||||||||||||||
1.10 | −2.59267 | 3.00000 | −1.27808 | −19.3273 | −7.77800 | −18.8270 | 24.0550 | 9.00000 | 50.1091 | ||||||||||||||||||
1.11 | −2.13891 | 3.00000 | −3.42505 | 19.6067 | −6.41674 | −3.28131 | 24.4372 | 9.00000 | −41.9370 | ||||||||||||||||||
1.12 | −1.89451 | 3.00000 | −4.41082 | −1.56986 | −5.68354 | −16.4152 | 23.5125 | 9.00000 | 2.97412 | ||||||||||||||||||
1.13 | −1.62628 | 3.00000 | −5.35521 | 10.1067 | −4.87884 | −33.4720 | 21.7193 | 9.00000 | −16.4364 | ||||||||||||||||||
1.14 | −1.12653 | 3.00000 | −6.73092 | 7.04441 | −3.37960 | 27.2935 | 16.5949 | 9.00000 | −7.93577 | ||||||||||||||||||
1.15 | −0.758503 | 3.00000 | −7.42467 | −11.2678 | −2.27551 | 14.6463 | 11.6997 | 9.00000 | 8.54666 | ||||||||||||||||||
1.16 | −0.322279 | 3.00000 | −7.89614 | 14.3189 | −0.966836 | −0.273748 | 5.12299 | 9.00000 | −4.61468 | ||||||||||||||||||
1.17 | 0.0801108 | 3.00000 | −7.99358 | −13.1587 | 0.240332 | −10.8611 | −1.28126 | 9.00000 | −1.05416 | ||||||||||||||||||
1.18 | 0.414813 | 3.00000 | −7.82793 | −0.503347 | 1.24444 | −9.79226 | −6.56563 | 9.00000 | −0.208795 | ||||||||||||||||||
1.19 | 1.17903 | 3.00000 | −6.60988 | 5.70828 | 3.53710 | −7.52643 | −17.2255 | 9.00000 | 6.73025 | ||||||||||||||||||
1.20 | 1.27880 | 3.00000 | −6.36468 | 11.8772 | 3.83639 | −14.0141 | −18.3695 | 9.00000 | 15.1885 | ||||||||||||||||||
See all 31 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(-1\) |
\(23\) | \(-1\) |
\(29\) | \(-1\) |
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 | 2001.4.a.a | ✓ | 31 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
2001.4.a.a | ✓ | 31 | 1.a | even | 1 | 1 | trivial |