Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1502,4,Mod(1,1502)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1502, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1502.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1502 = 2 \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1502.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: | \(88.6208688286\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
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 | −2.00000 | −9.64515 | 4.00000 | −17.6721 | 19.2903 | 13.9621 | −8.00000 | 66.0289 | 35.3442 | ||||||||||||||||||
1.2 | −2.00000 | −9.59429 | 4.00000 | 15.5056 | 19.1886 | 10.1319 | −8.00000 | 65.0504 | −31.0112 | ||||||||||||||||||
1.3 | −2.00000 | −9.40572 | 4.00000 | 9.65316 | 18.8114 | −11.0514 | −8.00000 | 61.4676 | −19.3063 | ||||||||||||||||||
1.4 | −2.00000 | −8.36978 | 4.00000 | −6.70437 | 16.7396 | −12.8029 | −8.00000 | 43.0532 | 13.4087 | ||||||||||||||||||
1.5 | −2.00000 | −8.16529 | 4.00000 | −1.86828 | 16.3306 | −22.0940 | −8.00000 | 39.6719 | 3.73655 | ||||||||||||||||||
1.6 | −2.00000 | −7.61846 | 4.00000 | −21.5141 | 15.2369 | 6.54668 | −8.00000 | 31.0409 | 43.0283 | ||||||||||||||||||
1.7 | −2.00000 | −7.56481 | 4.00000 | −13.8274 | 15.1296 | −18.2002 | −8.00000 | 30.2264 | 27.6549 | ||||||||||||||||||
1.8 | −2.00000 | −7.28893 | 4.00000 | 18.5942 | 14.5779 | 26.5868 | −8.00000 | 26.1285 | −37.1883 | ||||||||||||||||||
1.9 | −2.00000 | −6.83728 | 4.00000 | 19.3533 | 13.6746 | −28.9038 | −8.00000 | 19.7484 | −38.7066 | ||||||||||||||||||
1.10 | −2.00000 | −6.74081 | 4.00000 | 4.55841 | 13.4816 | 2.39100 | −8.00000 | 18.4385 | −9.11683 | ||||||||||||||||||
1.11 | −2.00000 | −6.65183 | 4.00000 | 5.90777 | 13.3037 | 34.5897 | −8.00000 | 17.2468 | −11.8155 | ||||||||||||||||||
1.12 | −2.00000 | −5.97873 | 4.00000 | −4.86312 | 11.9575 | 7.19611 | −8.00000 | 8.74522 | 9.72623 | ||||||||||||||||||
1.13 | −2.00000 | −5.26714 | 4.00000 | 7.05284 | 10.5343 | 16.2931 | −8.00000 | 0.742754 | −14.1057 | ||||||||||||||||||
1.14 | −2.00000 | −4.62416 | 4.00000 | −16.9152 | 9.24832 | −6.35676 | −8.00000 | −5.61716 | 33.8304 | ||||||||||||||||||
1.15 | −2.00000 | −4.60042 | 4.00000 | −11.8069 | 9.20085 | 31.4184 | −8.00000 | −5.83610 | 23.6138 | ||||||||||||||||||
1.16 | −2.00000 | −4.02059 | 4.00000 | 5.63898 | 8.04117 | −3.56225 | −8.00000 | −10.8349 | −11.2780 | ||||||||||||||||||
1.17 | −2.00000 | −3.79236 | 4.00000 | −13.0979 | 7.58471 | 27.6803 | −8.00000 | −12.6180 | 26.1958 | ||||||||||||||||||
1.18 | −2.00000 | −2.48842 | 4.00000 | −0.779603 | 4.97683 | −32.8216 | −8.00000 | −20.8078 | 1.55921 | ||||||||||||||||||
1.19 | −2.00000 | −2.08855 | 4.00000 | 12.8128 | 4.17711 | 33.3668 | −8.00000 | −22.6379 | −25.6255 | ||||||||||||||||||
1.20 | −2.00000 | −1.77526 | 4.00000 | 3.05878 | 3.55052 | −14.9284 | −8.00000 | −23.8485 | −6.11756 | ||||||||||||||||||
See all 50 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
\(751\) | \(1\) |
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 | 1502.4.a.c | ✓ | 50 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1502.4.a.c | ✓ | 50 | 1.a | even | 1 | 1 | trivial |