Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6014,2,Mod(1,6014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6014 = 2 \cdot 31 \cdot 97 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6014.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: | \(48.0220317756\) |
Analytic rank: | \(1\) |
Dimension: | \(26\) |
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 | −1.00000 | −3.14014 | 1.00000 | 0.252814 | 3.14014 | 0.286115 | −1.00000 | 6.86045 | −0.252814 | ||||||||||||||||||
1.2 | −1.00000 | −2.80306 | 1.00000 | −2.82235 | 2.80306 | 1.54412 | −1.00000 | 4.85717 | 2.82235 | ||||||||||||||||||
1.3 | −1.00000 | −2.51408 | 1.00000 | 2.50556 | 2.51408 | 2.33554 | −1.00000 | 3.32060 | −2.50556 | ||||||||||||||||||
1.4 | −1.00000 | −2.47120 | 1.00000 | 2.48298 | 2.47120 | −0.497731 | −1.00000 | 3.10685 | −2.48298 | ||||||||||||||||||
1.5 | −1.00000 | −2.21781 | 1.00000 | −1.00012 | 2.21781 | −3.69279 | −1.00000 | 1.91869 | 1.00012 | ||||||||||||||||||
1.6 | −1.00000 | −1.63521 | 1.00000 | −1.12487 | 1.63521 | 4.58750 | −1.00000 | −0.326097 | 1.12487 | ||||||||||||||||||
1.7 | −1.00000 | −1.49307 | 1.00000 | −1.37361 | 1.49307 | 2.08128 | −1.00000 | −0.770731 | 1.37361 | ||||||||||||||||||
1.8 | −1.00000 | −1.39215 | 1.00000 | 4.11395 | 1.39215 | 3.54744 | −1.00000 | −1.06192 | −4.11395 | ||||||||||||||||||
1.9 | −1.00000 | −1.16238 | 1.00000 | 2.24255 | 1.16238 | −4.62620 | −1.00000 | −1.64888 | −2.24255 | ||||||||||||||||||
1.10 | −1.00000 | −1.15269 | 1.00000 | −2.51751 | 1.15269 | −3.14385 | −1.00000 | −1.67130 | 2.51751 | ||||||||||||||||||
1.11 | −1.00000 | −0.856174 | 1.00000 | −2.44143 | 0.856174 | −1.92686 | −1.00000 | −2.26697 | 2.44143 | ||||||||||||||||||
1.12 | −1.00000 | −0.416043 | 1.00000 | 1.65220 | 0.416043 | −1.29934 | −1.00000 | −2.82691 | −1.65220 | ||||||||||||||||||
1.13 | −1.00000 | −0.151357 | 1.00000 | −3.93367 | 0.151357 | −2.15644 | −1.00000 | −2.97709 | 3.93367 | ||||||||||||||||||
1.14 | −1.00000 | 0.0184050 | 1.00000 | 1.10015 | −0.0184050 | 2.72792 | −1.00000 | −2.99966 | −1.10015 | ||||||||||||||||||
1.15 | −1.00000 | 0.368779 | 1.00000 | 3.09038 | −0.368779 | −0.324140 | −1.00000 | −2.86400 | −3.09038 | ||||||||||||||||||
1.16 | −1.00000 | 0.597153 | 1.00000 | −1.55796 | −0.597153 | 1.79182 | −1.00000 | −2.64341 | 1.55796 | ||||||||||||||||||
1.17 | −1.00000 | 1.08164 | 1.00000 | −2.93532 | −1.08164 | 3.00815 | −1.00000 | −1.83006 | 2.93532 | ||||||||||||||||||
1.18 | −1.00000 | 1.31822 | 1.00000 | 0.162831 | −1.31822 | 0.466372 | −1.00000 | −1.26229 | −0.162831 | ||||||||||||||||||
1.19 | −1.00000 | 1.46607 | 1.00000 | 3.03124 | −1.46607 | −0.00838187 | −1.00000 | −0.850637 | −3.03124 | ||||||||||||||||||
1.20 | −1.00000 | 1.52491 | 1.00000 | 2.34910 | −1.52491 | −3.00840 | −1.00000 | −0.674664 | −2.34910 | ||||||||||||||||||
See all 26 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
\(31\) | \(1\) |
\(97\) | \(1\) |
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 | 6014.2.a.g | ✓ | 26 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6014.2.a.g | ✓ | 26 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{26} - 46 T_{3}^{24} - T_{3}^{23} + 916 T_{3}^{22} + 43 T_{3}^{21} - 10390 T_{3}^{20} - 783 T_{3}^{19} + \cdots - 88 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6014))\).