Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 717) |
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 | −5.30430 | 0 | 20.1356 | 1.74933 | 0 | −31.0971 | −64.3712 | 0 | −9.27899 | ||||||||||||||||||
1.2 | −4.86739 | 0 | 15.6914 | 12.8877 | 0 | 25.7021 | −37.4372 | 0 | −62.7292 | ||||||||||||||||||
1.3 | −4.68120 | 0 | 13.9136 | 9.12054 | 0 | −4.35896 | −27.6829 | 0 | −42.6951 | ||||||||||||||||||
1.4 | −4.21516 | 0 | 9.76757 | −14.1283 | 0 | −29.9315 | −7.45059 | 0 | 59.5530 | ||||||||||||||||||
1.5 | −3.99686 | 0 | 7.97490 | 10.1568 | 0 | 5.65927 | 0.100320 | 0 | −40.5954 | ||||||||||||||||||
1.6 | −3.64270 | 0 | 5.26927 | −14.5917 | 0 | 6.09065 | 9.94722 | 0 | 53.1530 | ||||||||||||||||||
1.7 | −3.55218 | 0 | 4.61801 | −1.20455 | 0 | 9.27993 | 12.0135 | 0 | 4.27878 | ||||||||||||||||||
1.8 | −3.15491 | 0 | 1.95344 | −4.03944 | 0 | 6.03808 | 19.0763 | 0 | 12.7440 | ||||||||||||||||||
1.9 | −1.61692 | 0 | −5.38557 | −9.90974 | 0 | −20.2386 | 21.6434 | 0 | 16.0233 | ||||||||||||||||||
1.10 | −1.48544 | 0 | −5.79347 | 10.1836 | 0 | 8.86157 | 20.4894 | 0 | −15.1271 | ||||||||||||||||||
1.11 | −1.36717 | 0 | −6.13085 | 15.7404 | 0 | 15.1668 | 19.3193 | 0 | −21.5198 | ||||||||||||||||||
1.12 | −0.915825 | 0 | −7.16127 | −7.54581 | 0 | 24.7091 | 13.8851 | 0 | 6.91064 | ||||||||||||||||||
1.13 | −0.889333 | 0 | −7.20909 | −6.34700 | 0 | −11.3318 | 13.5259 | 0 | 5.64460 | ||||||||||||||||||
1.14 | 0.410040 | 0 | −7.83187 | 19.1512 | 0 | −11.0347 | −6.49170 | 0 | 7.85278 | ||||||||||||||||||
1.15 | 0.609904 | 0 | −7.62802 | 11.6127 | 0 | −26.3682 | −9.53159 | 0 | 7.08263 | ||||||||||||||||||
1.16 | 0.709237 | 0 | −7.49698 | −22.0711 | 0 | −0.837973 | −10.9910 | 0 | −15.6536 | ||||||||||||||||||
1.17 | 1.15681 | 0 | −6.66179 | 10.4070 | 0 | 11.9554 | −16.9609 | 0 | 12.0389 | ||||||||||||||||||
1.18 | 1.62942 | 0 | −5.34499 | −14.4675 | 0 | −35.3781 | −21.7446 | 0 | −23.5737 | ||||||||||||||||||
1.19 | 2.22027 | 0 | −3.07038 | −14.7142 | 0 | 26.0557 | −24.5793 | 0 | −32.6696 | ||||||||||||||||||
1.20 | 3.21293 | 0 | 2.32293 | 16.5200 | 0 | −15.7443 | −18.2400 | 0 | 53.0777 | ||||||||||||||||||
See all 28 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(-1\) |
\(239\) | \(1\) |
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 | 2151.4.a.b | 28 | |
3.b | odd | 2 | 1 | 717.4.a.b | ✓ | 28 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
717.4.a.b | ✓ | 28 | 3.b | odd | 2 | 1 | |
2151.4.a.b | 28 | 1.a | even | 1 | 1 | trivial |