Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,23,Mod(6,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 23, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.6");
S:= CuspForms(chi, 23);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 23 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(107.347602195\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
6.1 | −4050.15 | − | 299643.i | 1.22094e7 | − | 2.18366e7i | 1.21360e9i | −1.56680e9 | + | 1.20622e9i | −3.24625e10 | −5.84046e10 | 8.84415e10i | ||||||||||||||
6.2 | −4050.15 | 299643.i | 1.22094e7 | 2.18366e7i | − | 1.21360e9i | −1.56680e9 | − | 1.20622e9i | −3.24625e10 | −5.84046e10 | − | 8.84415e10i | ||||||||||||||
6.3 | −3964.42 | − | 190565.i | 1.15223e7 | 2.18366e7i | 7.55481e8i | 1.88278e9 | − | 6.04124e8i | −2.90514e10 | −4.93408e9 | − | 8.65695e10i | ||||||||||||||
6.4 | −3964.42 | 190565.i | 1.15223e7 | − | 2.18366e7i | − | 7.55481e8i | 1.88278e9 | + | 6.04124e8i | −2.90514e10 | −4.93408e9 | 8.65695e10i | ||||||||||||||
6.5 | −3446.96 | 82840.2i | 7.68724e6 | − | 2.18366e7i | − | 2.85547e8i | −1.82094e9 | + | 7.70703e8i | −1.20400e10 | 2.45186e10 | 7.52699e10i | ||||||||||||||
6.6 | −3446.96 | − | 82840.2i | 7.68724e6 | 2.18366e7i | 2.85547e8i | −1.82094e9 | − | 7.70703e8i | −1.20400e10 | 2.45186e10 | − | 7.52699e10i | ||||||||||||||
6.7 | −3172.47 | 206326.i | 5.87023e6 | 2.18366e7i | − | 6.54561e8i | 1.61326e8 | + | 1.97073e9i | −5.31683e9 | −1.11893e10 | − | 6.92759e10i | ||||||||||||||
6.8 | −3172.47 | − | 206326.i | 5.87023e6 | − | 2.18366e7i | 6.54561e8i | 1.61326e8 | − | 1.97073e9i | −5.31683e9 | −1.11893e10 | 6.92759e10i | ||||||||||||||
6.9 | −2949.79 | − | 168176.i | 4.50698e6 | − | 2.18366e7i | 4.96086e8i | 1.79437e9 | + | 8.30701e8i | −9.22338e8 | 3.09777e9 | 6.44135e10i | ||||||||||||||
6.10 | −2949.79 | 168176.i | 4.50698e6 | 2.18366e7i | − | 4.96086e8i | 1.79437e9 | − | 8.30701e8i | −9.22338e8 | 3.09777e9 | − | 6.44135e10i | ||||||||||||||
6.11 | −2940.79 | − | 329816.i | 4.45397e6 | 2.18366e7i | 9.69921e8i | −1.99357e8 | − | 1.96725e9i | −7.63627e8 | −7.73975e10 | − | 6.42170e10i | ||||||||||||||
6.12 | −2940.79 | 329816.i | 4.45397e6 | − | 2.18366e7i | − | 9.69921e8i | −1.99357e8 | + | 1.96725e9i | −7.63627e8 | −7.73975e10 | 6.42170e10i | ||||||||||||||
6.13 | −2672.32 | − | 294572.i | 2.94698e6 | 2.18366e7i | 7.87191e8i | 1.00290e9 | + | 1.70411e9i | 3.33326e9 | −5.53919e10 | − | 5.83543e10i | ||||||||||||||
6.14 | −2672.32 | 294572.i | 2.94698e6 | − | 2.18366e7i | − | 7.87191e8i | 1.00290e9 | − | 1.70411e9i | 3.33326e9 | −5.53919e10 | 5.83543e10i | ||||||||||||||
6.15 | −2054.98 | 104363.i | 28626.0 | − | 2.18366e7i | − | 2.14463e8i | −1.43402e9 | − | 1.36139e9i | 8.56037e9 | 2.04895e10 | 4.48737e10i | ||||||||||||||
6.16 | −2054.98 | − | 104363.i | 28626.0 | 2.18366e7i | 2.14463e8i | −1.43402e9 | + | 1.36139e9i | 8.56037e9 | 2.04895e10 | − | 4.48737e10i | ||||||||||||||
6.17 | −1882.46 | − | 2834.26i | −650663. | − | 2.18366e7i | 5.33538e6i | −7.86883e8 | + | 1.81401e9i | 9.12044e9 | 3.13730e10 | 4.11064e10i | ||||||||||||||
6.18 | −1882.46 | 2834.26i | −650663. | 2.18366e7i | − | 5.33538e6i | −7.86883e8 | − | 1.81401e9i | 9.12044e9 | 3.13730e10 | − | 4.11064e10i | ||||||||||||||
6.19 | −1783.43 | − | 46763.5i | −1.01367e6 | 2.18366e7i | 8.33995e7i | 1.78330e9 | − | 8.54211e8i | 9.28808e9 | 2.91942e10 | − | 3.89441e10i | ||||||||||||||
6.20 | −1783.43 | 46763.5i | −1.01367e6 | − | 2.18366e7i | − | 8.33995e7i | 1.78330e9 | + | 8.54211e8i | 9.28808e9 | 2.91942e10 | 3.89441e10i | ||||||||||||||
See all 60 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
7.b | odd | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 35.23.d.a | ✓ | 60 |
7.b | odd | 2 | 1 | inner | 35.23.d.a | ✓ | 60 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
35.23.d.a | ✓ | 60 | 1.a | even | 1 | 1 | trivial |
35.23.d.a | ✓ | 60 | 7.b | odd | 2 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{23}^{\mathrm{new}}(35, [\chi])\).