Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, 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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(1\) |
Dimension: | \(153\) |
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 | −2.82377 | 0.0811365 | 5.97367 | 1.22528 | −0.229111 | 1.93678 | −11.2207 | −2.99342 | −3.45990 | ||||||||||||||||||
1.2 | −2.76122 | −1.93941 | 5.62432 | −0.205414 | 5.35515 | −1.99038 | −10.0076 | 0.761331 | 0.567192 | ||||||||||||||||||
1.3 | −2.72579 | 2.89515 | 5.42994 | −2.27822 | −7.89157 | −3.84210 | −9.34930 | 5.38188 | 6.20996 | ||||||||||||||||||
1.4 | −2.71996 | −3.40952 | 5.39818 | 0.859174 | 9.27375 | 3.37109 | −9.24292 | 8.62480 | −2.33692 | ||||||||||||||||||
1.5 | −2.64082 | 1.90424 | 4.97394 | 2.87158 | −5.02877 | 0.865912 | −7.85365 | 0.626146 | −7.58334 | ||||||||||||||||||
1.6 | −2.62408 | −2.48215 | 4.88578 | −3.25865 | 6.51336 | 0.610888 | −7.57250 | 3.16108 | 8.55094 | ||||||||||||||||||
1.7 | −2.55787 | −0.498344 | 4.54269 | 3.86602 | 1.27470 | −1.47646 | −6.50388 | −2.75165 | −9.88878 | ||||||||||||||||||
1.8 | −2.55291 | −0.169380 | 4.51736 | −0.762748 | 0.432413 | 0.998481 | −6.42660 | −2.97131 | 1.94723 | ||||||||||||||||||
1.9 | −2.54449 | −2.75216 | 4.47442 | −0.0821866 | 7.00285 | −2.51361 | −6.29612 | 4.57441 | 0.209123 | ||||||||||||||||||
1.10 | −2.53517 | 1.42230 | 4.42707 | −0.780530 | −3.60576 | 3.78955 | −6.15303 | −0.977076 | 1.97877 | ||||||||||||||||||
1.11 | −2.49383 | −0.270355 | 4.21918 | −2.99495 | 0.674220 | −3.80387 | −5.53426 | −2.92691 | 7.46890 | ||||||||||||||||||
1.12 | −2.46809 | 2.55539 | 4.09144 | 0.103837 | −6.30691 | 0.172456 | −5.16186 | 3.53000 | −0.256278 | ||||||||||||||||||
1.13 | −2.45028 | −2.96227 | 4.00387 | −1.96635 | 7.25838 | −3.26353 | −4.91003 | 5.77502 | 4.81810 | ||||||||||||||||||
1.14 | −2.41716 | −1.38399 | 3.84266 | 1.63498 | 3.34533 | −3.98295 | −4.45401 | −1.08457 | −3.95202 | ||||||||||||||||||
1.15 | −2.40368 | 2.42213 | 3.77770 | 1.57847 | −5.82205 | −3.75128 | −4.27303 | 2.86673 | −3.79414 | ||||||||||||||||||
1.16 | −2.36991 | −1.12262 | 3.61648 | 0.983312 | 2.66051 | 2.71051 | −3.83091 | −1.73972 | −2.33036 | ||||||||||||||||||
1.17 | −2.35186 | 2.82673 | 3.53125 | 2.18646 | −6.64808 | 0.649269 | −3.60130 | 4.99041 | −5.14224 | ||||||||||||||||||
1.18 | −2.34979 | −2.55203 | 3.52153 | 3.27958 | 5.99675 | 4.82178 | −3.57528 | 3.51287 | −7.70633 | ||||||||||||||||||
1.19 | −2.34552 | 3.15214 | 3.50145 | −3.97132 | −7.39341 | −1.04283 | −3.52168 | 6.93601 | 9.31479 | ||||||||||||||||||
1.20 | −2.32654 | −0.105675 | 3.41278 | −1.05522 | 0.245856 | 0.945293 | −3.28688 | −2.98883 | 2.45502 | ||||||||||||||||||
See next 80 embeddings (of 153 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(53\) | \(1\) |
\(151\) | \(1\) |
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 | 8003.2.a.b | ✓ | 153 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8003.2.a.b | ✓ | 153 | 1.a | even | 1 | 1 | trivial |