Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7935,2,Mod(1,7935)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7935, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7935.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7935 = 3 \cdot 5 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7935.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: | \(63.3612940039\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | no (minimal twist has level 345) |
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 | −2.37846 | 1.00000 | 3.65709 | 1.00000 | −2.37846 | −2.06593 | −3.94134 | 1.00000 | −2.37846 | ||||||||||||||||||
1.2 | −2.29641 | 1.00000 | 3.27349 | 1.00000 | −2.29641 | −2.28611 | −2.92446 | 1.00000 | −2.29641 | ||||||||||||||||||
1.3 | −2.21783 | 1.00000 | 2.91878 | 1.00000 | −2.21783 | −1.19670 | −2.03770 | 1.00000 | −2.21783 | ||||||||||||||||||
1.4 | −2.00202 | 1.00000 | 2.00810 | 1.00000 | −2.00202 | 3.16837 | −0.0162194 | 1.00000 | −2.00202 | ||||||||||||||||||
1.5 | −1.35850 | 1.00000 | −0.154487 | 1.00000 | −1.35850 | 1.13918 | 2.92686 | 1.00000 | −1.35850 | ||||||||||||||||||
1.6 | −1.21693 | 1.00000 | −0.519082 | 1.00000 | −1.21693 | −3.32401 | 3.06555 | 1.00000 | −1.21693 | ||||||||||||||||||
1.7 | −1.17495 | 1.00000 | −0.619503 | 1.00000 | −1.17495 | 4.87740 | 3.07777 | 1.00000 | −1.17495 | ||||||||||||||||||
1.8 | −1.08036 | 1.00000 | −0.832828 | 1.00000 | −1.08036 | 2.50098 | 3.06047 | 1.00000 | −1.08036 | ||||||||||||||||||
1.9 | −0.404849 | 1.00000 | −1.83610 | 1.00000 | −0.404849 | 1.25801 | 1.55304 | 1.00000 | −0.404849 | ||||||||||||||||||
1.10 | −0.358480 | 1.00000 | −1.87149 | 1.00000 | −0.358480 | −2.43554 | 1.38785 | 1.00000 | −0.358480 | ||||||||||||||||||
1.11 | 0.117537 | 1.00000 | −1.98618 | 1.00000 | 0.117537 | −2.82367 | −0.468525 | 1.00000 | 0.117537 | ||||||||||||||||||
1.12 | 0.134140 | 1.00000 | −1.98201 | 1.00000 | 0.134140 | 1.40831 | −0.534145 | 1.00000 | 0.134140 | ||||||||||||||||||
1.13 | 0.872240 | 1.00000 | −1.23920 | 1.00000 | 0.872240 | 3.30692 | −2.82536 | 1.00000 | 0.872240 | ||||||||||||||||||
1.14 | 0.940321 | 1.00000 | −1.11580 | 1.00000 | 0.940321 | 0.900767 | −2.92985 | 1.00000 | 0.940321 | ||||||||||||||||||
1.15 | 1.14392 | 1.00000 | −0.691452 | 1.00000 | 1.14392 | 1.05238 | −3.07880 | 1.00000 | 1.14392 | ||||||||||||||||||
1.16 | 1.40188 | 1.00000 | −0.0347196 | 1.00000 | 1.40188 | −5.24426 | −2.85244 | 1.00000 | 1.40188 | ||||||||||||||||||
1.17 | 1.50967 | 1.00000 | 0.279113 | 1.00000 | 1.50967 | 2.29097 | −2.59798 | 1.00000 | 1.50967 | ||||||||||||||||||
1.18 | 1.96315 | 1.00000 | 1.85395 | 1.00000 | 1.96315 | 4.65397 | −0.286724 | 1.00000 | 1.96315 | ||||||||||||||||||
1.19 | 2.02762 | 1.00000 | 2.11124 | 1.00000 | 2.02762 | 3.74723 | 0.225557 | 1.00000 | 2.02762 | ||||||||||||||||||
1.20 | 2.03825 | 1.00000 | 2.15445 | 1.00000 | 2.03825 | −3.70333 | 0.314810 | 1.00000 | 2.03825 | ||||||||||||||||||
See all 25 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(-1\) |
\(5\) | \(-1\) |
\(23\) | \(-1\) |
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 | 7935.2.a.bw | 25 | |
23.b | odd | 2 | 1 | 7935.2.a.bv | 25 | ||
23.d | odd | 22 | 2 | 345.2.m.c | ✓ | 50 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
345.2.m.c | ✓ | 50 | 23.d | odd | 22 | 2 | |
7935.2.a.bv | 25 | 23.b | odd | 2 | 1 | ||
7935.2.a.bw | 25 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7935))\):
\( T_{2}^{25} - 11 T_{2}^{24} + 20 T_{2}^{23} + 198 T_{2}^{22} - 844 T_{2}^{21} - 836 T_{2}^{20} + \cdots - 253 \) |
\( T_{7}^{25} - 7 T_{7}^{24} - 83 T_{7}^{23} + 644 T_{7}^{22} + 2739 T_{7}^{21} - 24826 T_{7}^{20} + \cdots - 902144 \) |
\( T_{11}^{25} - 9 T_{11}^{24} - 126 T_{11}^{23} + 1329 T_{11}^{22} + 5698 T_{11}^{21} - 80067 T_{11}^{20} + \cdots - 106714112 \) |