Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6023,2,Mod(1,6023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6023, 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("6023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6023 = 19 \cdot 317 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6023.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: | \(48.0938971374\) |
Analytic rank: | \(0\) |
Dimension: | \(138\) |
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 | −2.80790 | 2.44752 | 5.88430 | 0.306657 | −6.87238 | −4.87771 | −10.9067 | 2.99034 | −0.861061 | ||||||||||||||||||
1.2 | −2.76304 | −0.570737 | 5.63440 | 2.36853 | 1.57697 | 1.21818 | −10.0420 | −2.67426 | −6.54436 | ||||||||||||||||||
1.3 | −2.74148 | −0.0386597 | 5.51569 | −1.76662 | 0.105985 | 3.31998 | −9.63818 | −2.99851 | 4.84315 | ||||||||||||||||||
1.4 | −2.68395 | 2.15160 | 5.20359 | 1.49960 | −5.77479 | 0.747166 | −8.59827 | 1.62938 | −4.02486 | ||||||||||||||||||
1.5 | −2.67199 | 3.08563 | 5.13955 | −4.31422 | −8.24478 | 2.33147 | −8.38886 | 6.52111 | 11.5276 | ||||||||||||||||||
1.6 | −2.67164 | −1.61720 | 5.13764 | −4.16220 | 4.32056 | −1.04033 | −8.38264 | −0.384677 | 11.1199 | ||||||||||||||||||
1.7 | −2.58182 | −0.634269 | 4.66582 | 2.08330 | 1.63757 | 3.68872 | −6.88267 | −2.59770 | −5.37871 | ||||||||||||||||||
1.8 | −2.57032 | −2.26358 | 4.60652 | −0.389233 | 5.81812 | 0.261062 | −6.69959 | 2.12381 | 1.00045 | ||||||||||||||||||
1.9 | −2.56824 | −3.23259 | 4.59584 | −2.23172 | 8.30205 | 3.00174 | −6.66674 | 7.44963 | 5.73158 | ||||||||||||||||||
1.10 | −2.53137 | 2.03677 | 4.40782 | 3.56698 | −5.15582 | −0.371412 | −6.09508 | 1.14845 | −9.02935 | ||||||||||||||||||
1.11 | −2.51157 | 0.714819 | 4.30797 | −1.12509 | −1.79532 | −0.994631 | −5.79662 | −2.48903 | 2.82573 | ||||||||||||||||||
1.12 | −2.40954 | 1.37728 | 3.80590 | −2.93809 | −3.31862 | −1.98041 | −4.35139 | −1.10309 | 7.07945 | ||||||||||||||||||
1.13 | −2.39602 | −1.69365 | 3.74091 | −0.534671 | 4.05801 | −0.0216661 | −4.17126 | −0.131565 | 1.28108 | ||||||||||||||||||
1.14 | −2.39507 | 3.00458 | 3.73634 | −1.01813 | −7.19617 | −4.72960 | −4.15865 | 6.02752 | 2.43848 | ||||||||||||||||||
1.15 | −2.33668 | 3.18243 | 3.46006 | 4.06905 | −7.43630 | 5.05493 | −3.41169 | 7.12783 | −9.50807 | ||||||||||||||||||
1.16 | −2.26801 | 0.709403 | 3.14388 | −4.17389 | −1.60894 | 3.35218 | −2.59433 | −2.49675 | 9.46643 | ||||||||||||||||||
1.17 | −2.24651 | −2.33680 | 3.04682 | 3.03120 | 5.24966 | −0.990135 | −2.35169 | 2.46065 | −6.80962 | ||||||||||||||||||
1.18 | −2.22566 | −1.96365 | 2.95355 | 3.43373 | 4.37041 | −3.81546 | −2.12228 | 0.855918 | −7.64232 | ||||||||||||||||||
1.19 | −2.22132 | 1.60897 | 2.93428 | 0.172135 | −3.57405 | −2.94325 | −2.07533 | −0.411206 | −0.382368 | ||||||||||||||||||
1.20 | −2.14132 | 0.0864735 | 2.58523 | 2.84531 | −0.185167 | 1.71112 | −1.25317 | −2.99252 | −6.09271 | ||||||||||||||||||
See next 80 embeddings (of 138 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(19\) | \(-1\) |
\(317\) | \(1\) |
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 | 6023.2.a.c | ✓ | 138 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6023.2.a.c | ✓ | 138 | 1.a | even | 1 | 1 | trivial |