Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,4,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, 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("1875.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(110.628581261\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
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 | −5.63525 | −3.00000 | 23.7560 | 0 | 16.9058 | 12.9594 | −88.7893 | 9.00000 | 0 | ||||||||||||||||||
1.2 | −5.42895 | −3.00000 | 21.4736 | 0 | 16.2869 | −15.6883 | −73.1473 | 9.00000 | 0 | ||||||||||||||||||
1.3 | −5.20860 | −3.00000 | 19.1295 | 0 | 15.6258 | −35.1109 | −57.9692 | 9.00000 | 0 | ||||||||||||||||||
1.4 | −4.82486 | −3.00000 | 15.2792 | 0 | 14.4746 | −14.5960 | −35.1213 | 9.00000 | 0 | ||||||||||||||||||
1.5 | −3.88504 | −3.00000 | 7.09353 | 0 | 11.6551 | 27.2564 | 3.52166 | 9.00000 | 0 | ||||||||||||||||||
1.6 | −3.33280 | −3.00000 | 3.10756 | 0 | 9.99840 | −15.5967 | 16.3055 | 9.00000 | 0 | ||||||||||||||||||
1.7 | −2.99872 | −3.00000 | 0.992297 | 0 | 8.99615 | 35.4081 | 21.0141 | 9.00000 | 0 | ||||||||||||||||||
1.8 | −2.99444 | −3.00000 | 0.966662 | 0 | 8.98332 | 20.0639 | 21.0609 | 9.00000 | 0 | ||||||||||||||||||
1.9 | −2.67175 | −3.00000 | −0.861747 | 0 | 8.01525 | −25.7294 | 23.6764 | 9.00000 | 0 | ||||||||||||||||||
1.10 | −1.22991 | −3.00000 | −6.48731 | 0 | 3.68974 | −22.2749 | 17.8181 | 9.00000 | 0 | ||||||||||||||||||
1.11 | −0.896911 | −3.00000 | −7.19555 | 0 | 2.69073 | −28.1780 | 13.6291 | 9.00000 | 0 | ||||||||||||||||||
1.12 | −0.234134 | −3.00000 | −7.94518 | 0 | 0.702403 | 2.94104 | 3.73331 | 9.00000 | 0 | ||||||||||||||||||
1.13 | 0.382314 | −3.00000 | −7.85384 | 0 | −1.14694 | 13.0193 | −6.06115 | 9.00000 | 0 | ||||||||||||||||||
1.14 | 0.487528 | −3.00000 | −7.76232 | 0 | −1.46258 | 9.19148 | −7.68457 | 9.00000 | 0 | ||||||||||||||||||
1.15 | 0.848785 | −3.00000 | −7.27956 | 0 | −2.54636 | −4.78585 | −12.9691 | 9.00000 | 0 | ||||||||||||||||||
1.16 | 2.12561 | −3.00000 | −3.48177 | 0 | −6.37684 | −8.29876 | −24.4058 | 9.00000 | 0 | ||||||||||||||||||
1.17 | 3.24482 | −3.00000 | 2.52885 | 0 | −9.73446 | −6.19089 | −17.7529 | 9.00000 | 0 | ||||||||||||||||||
1.18 | 3.31176 | −3.00000 | 2.96774 | 0 | −9.93527 | −17.0520 | −16.6656 | 9.00000 | 0 | ||||||||||||||||||
1.19 | 3.80799 | −3.00000 | 6.50079 | 0 | −11.4240 | 18.9068 | −5.70897 | 9.00000 | 0 | ||||||||||||||||||
1.20 | 3.84470 | −3.00000 | 6.78175 | 0 | −11.5341 | 25.3925 | −4.68382 | 9.00000 | 0 | ||||||||||||||||||
See all 24 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(1\) |
\(5\) | \(1\) |
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 | 1875.4.a.k | ✓ | 24 |
5.b | even | 2 | 1 | 1875.4.a.l | yes | 24 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1875.4.a.k | ✓ | 24 | 1.a | even | 1 | 1 | trivial |
1875.4.a.l | yes | 24 | 5.b | even | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} + T_{2}^{23} - 162 T_{2}^{22} - 148 T_{2}^{21} + 11359 T_{2}^{20} + 9556 T_{2}^{19} + \cdots + 2143086336 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1875))\).