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 | −2.70525 | −1.00000 | 5.31837 | −1.00000 | 2.70525 | −1.20644 | −8.97700 | 1.00000 | 2.70525 | ||||||||||||||||||
1.2 | −2.56809 | −1.00000 | 4.59508 | −1.00000 | 2.56809 | 4.04574 | −6.66440 | 1.00000 | 2.56809 | ||||||||||||||||||
1.3 | −2.52606 | −1.00000 | 4.38100 | −1.00000 | 2.52606 | 3.87823 | −6.01456 | 1.00000 | 2.52606 | ||||||||||||||||||
1.4 | −2.18378 | −1.00000 | 2.76889 | −1.00000 | 2.18378 | 0.993609 | −1.67909 | 1.00000 | 2.18378 | ||||||||||||||||||
1.5 | −2.08135 | −1.00000 | 2.33203 | −1.00000 | 2.08135 | −4.74881 | −0.691076 | 1.00000 | 2.08135 | ||||||||||||||||||
1.6 | −1.81497 | −1.00000 | 1.29411 | −1.00000 | 1.81497 | 4.23294 | 1.28116 | 1.00000 | 1.81497 | ||||||||||||||||||
1.7 | −1.51687 | −1.00000 | 0.300900 | −1.00000 | 1.51687 | 3.34169 | 2.57732 | 1.00000 | 1.51687 | ||||||||||||||||||
1.8 | −1.42787 | −1.00000 | 0.0388086 | −1.00000 | 1.42787 | −1.25355 | 2.80032 | 1.00000 | 1.42787 | ||||||||||||||||||
1.9 | −1.21553 | −1.00000 | −0.522493 | −1.00000 | 1.21553 | −3.08881 | 3.06616 | 1.00000 | 1.21553 | ||||||||||||||||||
1.10 | −0.688592 | −1.00000 | −1.52584 | −1.00000 | 0.688592 | 4.50249 | 2.42787 | 1.00000 | 0.688592 | ||||||||||||||||||
1.11 | −0.587229 | −1.00000 | −1.65516 | −1.00000 | 0.587229 | −1.98135 | 2.14642 | 1.00000 | 0.587229 | ||||||||||||||||||
1.12 | 0.0244504 | −1.00000 | −1.99940 | −1.00000 | −0.0244504 | −1.12043 | −0.0977870 | 1.00000 | −0.0244504 | ||||||||||||||||||
1.13 | 0.137935 | −1.00000 | −1.98097 | −1.00000 | −0.137935 | −4.46257 | −0.549115 | 1.00000 | −0.137935 | ||||||||||||||||||
1.14 | 0.185184 | −1.00000 | −1.96571 | −1.00000 | −0.185184 | 4.18574 | −0.734387 | 1.00000 | −0.185184 | ||||||||||||||||||
1.15 | 0.535974 | −1.00000 | −1.71273 | −1.00000 | −0.535974 | 1.69269 | −1.98993 | 1.00000 | −0.535974 | ||||||||||||||||||
1.16 | 0.902689 | −1.00000 | −1.18515 | −1.00000 | −0.902689 | −0.451264 | −2.87520 | 1.00000 | −0.902689 | ||||||||||||||||||
1.17 | 1.28657 | −1.00000 | −0.344734 | −1.00000 | −1.28657 | 0.187319 | −3.01667 | 1.00000 | −1.28657 | ||||||||||||||||||
1.18 | 1.50246 | −1.00000 | 0.257377 | −1.00000 | −1.50246 | 4.80829 | −2.61822 | 1.00000 | −1.50246 | ||||||||||||||||||
1.19 | 1.59695 | −1.00000 | 0.550248 | −1.00000 | −1.59695 | −3.15385 | −2.31518 | 1.00000 | −1.59695 | ||||||||||||||||||
1.20 | 1.79106 | −1.00000 | 1.20789 | −1.00000 | −1.79106 | 4.79732 | −1.41871 | 1.00000 | −1.79106 | ||||||||||||||||||
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.bt | 25 | |
23.b | odd | 2 | 1 | 7935.2.a.bu | 25 | ||
23.d | odd | 22 | 2 | 345.2.m.d | ✓ | 50 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
345.2.m.d | ✓ | 50 | 23.d | odd | 22 | 2 | |
7935.2.a.bt | 25 | 1.a | even | 1 | 1 | trivial | |
7935.2.a.bu | 25 | 23.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7935))\):
\( T_{2}^{25} - T_{2}^{24} - 40 T_{2}^{23} + 38 T_{2}^{22} + 696 T_{2}^{21} - 626 T_{2}^{20} - 6918 T_{2}^{19} + \cdots + 23 \) |
\( T_{7}^{25} - 15 T_{7}^{24} - 21 T_{7}^{23} + 1318 T_{7}^{22} - 3341 T_{7}^{21} - 46190 T_{7}^{20} + \cdots - 564517888 \) |
\( T_{11}^{25} + 15 T_{11}^{24} - 80 T_{11}^{23} - 2221 T_{11}^{22} - 1858 T_{11}^{21} + \cdots - 456373351424 \) |