Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3013,2,Mod(1,3013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3013, 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("3013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3013 = 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3013.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: | \(24.0589261290\) |
Analytic rank: | \(1\) |
Dimension: | \(60\) |
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 | −2.79587 | −2.97360 | 5.81687 | −2.51130 | 8.31379 | 4.67754 | −10.6715 | 5.84229 | 7.02127 | ||||||||||||||||||
1.2 | −2.71521 | −0.598214 | 5.37236 | −3.83643 | 1.62427 | −2.75462 | −9.15665 | −2.64214 | 10.4167 | ||||||||||||||||||
1.3 | −2.62803 | 2.41455 | 4.90653 | −1.08370 | −6.34551 | 0.602139 | −7.63843 | 2.83006 | 2.84798 | ||||||||||||||||||
1.4 | −2.62629 | 1.77781 | 4.89739 | −0.230158 | −4.66905 | −4.80761 | −7.60937 | 0.160624 | 0.604460 | ||||||||||||||||||
1.5 | −2.58498 | −3.19298 | 4.68213 | 4.05739 | 8.25380 | −2.42165 | −6.93326 | 7.19512 | −10.4883 | ||||||||||||||||||
1.6 | −2.56642 | −1.77721 | 4.58651 | 0.593660 | 4.56108 | 1.47002 | −6.63807 | 0.158488 | −1.52358 | ||||||||||||||||||
1.7 | −2.55997 | −0.479961 | 4.55347 | −1.89513 | 1.22869 | 2.74253 | −6.53680 | −2.76964 | 4.85149 | ||||||||||||||||||
1.8 | −2.40558 | −1.92442 | 3.78680 | 3.01488 | 4.62933 | −3.47142 | −4.29827 | 0.703380 | −7.25251 | ||||||||||||||||||
1.9 | −2.30239 | 2.95532 | 3.30101 | −2.07600 | −6.80430 | 2.92187 | −2.99543 | 5.73391 | 4.77977 | ||||||||||||||||||
1.10 | −2.22304 | −1.10362 | 2.94190 | 1.61742 | 2.45339 | 2.04803 | −2.09388 | −1.78202 | −3.59560 | ||||||||||||||||||
1.11 | −2.22096 | 1.35059 | 2.93267 | 3.03988 | −2.99961 | 1.15220 | −2.07143 | −1.17591 | −6.75145 | ||||||||||||||||||
1.12 | −2.04946 | 0.601579 | 2.20030 | −3.41899 | −1.23291 | 2.94706 | −0.410502 | −2.63810 | 7.00710 | ||||||||||||||||||
1.13 | −2.02481 | −3.10292 | 2.09986 | −2.00579 | 6.28282 | 1.72430 | −0.202204 | 6.62809 | 4.06134 | ||||||||||||||||||
1.14 | −1.98054 | 1.15931 | 1.92256 | 3.44618 | −2.29606 | 0.529590 | 0.153377 | −1.65601 | −6.82531 | ||||||||||||||||||
1.15 | −1.87019 | −0.405783 | 1.49763 | −0.982634 | 0.758892 | −0.911232 | 0.939538 | −2.83534 | 1.83772 | ||||||||||||||||||
1.16 | −1.69333 | −1.67284 | 0.867373 | 1.34549 | 2.83267 | 1.81560 | 1.91791 | −0.201619 | −2.27837 | ||||||||||||||||||
1.17 | −1.66222 | 2.03520 | 0.762984 | 1.32690 | −3.38296 | −3.56689 | 2.05620 | 1.14205 | −2.20560 | ||||||||||||||||||
1.18 | −1.51615 | −0.884449 | 0.298703 | −4.02719 | 1.34096 | −3.85486 | 2.57942 | −2.21775 | 6.10582 | ||||||||||||||||||
1.19 | −1.42107 | −3.07912 | 0.0194373 | 0.905081 | 4.37564 | −3.86972 | 2.81452 | 6.48099 | −1.28618 | ||||||||||||||||||
1.20 | −1.31053 | 0.397123 | −0.282513 | 3.32742 | −0.520442 | −4.72120 | 2.99130 | −2.84229 | −4.36068 | ||||||||||||||||||
See all 60 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(23\) | \(1\) |
\(131\) | \(1\) |
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 | 3013.2.a.c | ✓ | 60 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
3013.2.a.c | ✓ | 60 | 1.a | even | 1 | 1 | trivial |