Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6035,2,Mod(1,6035)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6035, 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("6035.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6035 = 5 \cdot 17 \cdot 71 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6035.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: | \(48.1897176198\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
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 | −2.70980 | −1.97129 | 5.34301 | −1.00000 | 5.34180 | −3.23556 | −9.05887 | 0.885985 | 2.70980 | ||||||||||||||||||
1.2 | −2.65545 | 0.992184 | 5.05140 | −1.00000 | −2.63469 | 2.21189 | −8.10282 | −2.01557 | 2.65545 | ||||||||||||||||||
1.3 | −2.58454 | 0.349560 | 4.67987 | −1.00000 | −0.903452 | −2.04775 | −6.92624 | −2.87781 | 2.58454 | ||||||||||||||||||
1.4 | −2.43809 | 2.70086 | 3.94428 | −1.00000 | −6.58493 | −4.52426 | −4.74032 | 4.29464 | 2.43809 | ||||||||||||||||||
1.5 | −2.35000 | 1.53391 | 3.52249 | −1.00000 | −3.60469 | 3.64205 | −3.57785 | −0.647109 | 2.35000 | ||||||||||||||||||
1.6 | −2.32691 | −2.96703 | 3.41452 | −1.00000 | 6.90401 | 1.40727 | −3.29145 | 5.80324 | 2.32691 | ||||||||||||||||||
1.7 | −2.01551 | 2.29705 | 2.06228 | −1.00000 | −4.62973 | 2.65647 | −0.125520 | 2.27646 | 2.01551 | ||||||||||||||||||
1.8 | −1.90874 | −1.84827 | 1.64328 | −1.00000 | 3.52785 | −4.00780 | 0.680888 | 0.416086 | 1.90874 | ||||||||||||||||||
1.9 | −1.83345 | −1.98397 | 1.36153 | −1.00000 | 3.63750 | 3.16158 | 1.17060 | 0.936121 | 1.83345 | ||||||||||||||||||
1.10 | −1.82282 | −3.34912 | 1.32269 | −1.00000 | 6.10486 | −3.68631 | 1.23462 | 8.21664 | 1.82282 | ||||||||||||||||||
1.11 | −1.63791 | 2.24378 | 0.682749 | −1.00000 | −3.67512 | −2.25515 | 2.15754 | 2.03457 | 1.63791 | ||||||||||||||||||
1.12 | −1.60438 | −0.0375345 | 0.574038 | −1.00000 | 0.0602197 | 0.265901 | 2.28779 | −2.99859 | 1.60438 | ||||||||||||||||||
1.13 | −1.46835 | −1.29566 | 0.156056 | −1.00000 | 1.90248 | 2.74106 | 2.70756 | −1.32128 | 1.46835 | ||||||||||||||||||
1.14 | −1.35784 | 0.0329488 | −0.156280 | −1.00000 | −0.0447392 | −2.89786 | 2.92788 | −2.99891 | 1.35784 | ||||||||||||||||||
1.15 | −1.09248 | 1.17404 | −0.806486 | −1.00000 | −1.28261 | −2.18845 | 3.06603 | −1.62164 | 1.09248 | ||||||||||||||||||
1.16 | −0.962995 | 1.93597 | −1.07264 | −1.00000 | −1.86433 | −0.00468227 | 2.95894 | 0.747980 | 0.962995 | ||||||||||||||||||
1.17 | −0.731776 | −2.99784 | −1.46450 | −1.00000 | 2.19375 | 0.653628 | 2.53524 | 5.98707 | 0.731776 | ||||||||||||||||||
1.18 | −0.668824 | 1.88540 | −1.55267 | −1.00000 | −1.26100 | 1.98654 | 2.37611 | 0.554720 | 0.668824 | ||||||||||||||||||
1.19 | −0.546289 | −0.826758 | −1.70157 | −1.00000 | 0.451649 | 2.37358 | 2.02213 | −2.31647 | 0.546289 | ||||||||||||||||||
1.20 | −0.529049 | 3.17925 | −1.72011 | −1.00000 | −1.68198 | −0.889199 | 1.96812 | 7.10763 | 0.529049 | ||||||||||||||||||
See all 44 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(5\) | \(1\) |
\(17\) | \(-1\) |
\(71\) | \(-1\) |
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 | 6035.2.a.d | ✓ | 44 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6035.2.a.d | ✓ | 44 | 1.a | even | 1 | 1 | trivial |