Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4527,2,Mod(1,4527)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4527, 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("4527.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4527 = 3^{2} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4527.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: | \(36.1482769950\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | no (minimal twist has level 503) |
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 | −2.71305 | 0 | 5.36063 | 1.98731 | 0 | 2.61319 | −9.11755 | 0 | −5.39167 | ||||||||||||||||||
1.2 | −2.66972 | 0 | 5.12740 | −2.58453 | 0 | −2.90918 | −8.34929 | 0 | 6.89997 | ||||||||||||||||||
1.3 | −2.58315 | 0 | 4.67265 | 4.14994 | 0 | −3.36863 | −6.90384 | 0 | −10.7199 | ||||||||||||||||||
1.4 | −2.45386 | 0 | 4.02143 | −1.44250 | 0 | 0.736665 | −4.96031 | 0 | 3.53970 | ||||||||||||||||||
1.5 | −2.36292 | 0 | 3.58340 | −0.763844 | 0 | −0.178001 | −3.74145 | 0 | 1.80490 | ||||||||||||||||||
1.6 | −2.34577 | 0 | 3.50263 | 2.04978 | 0 | 4.12271 | −3.52482 | 0 | −4.80830 | ||||||||||||||||||
1.7 | −1.88946 | 0 | 1.57004 | −3.67682 | 0 | 1.62501 | 0.812389 | 0 | 6.94719 | ||||||||||||||||||
1.8 | −1.81497 | 0 | 1.29413 | −2.10638 | 0 | 1.73516 | 1.28114 | 0 | 3.82302 | ||||||||||||||||||
1.9 | −1.61798 | 0 | 0.617860 | −3.34245 | 0 | −5.14301 | 2.23628 | 0 | 5.40802 | ||||||||||||||||||
1.10 | −1.26316 | 0 | −0.404427 | 4.34050 | 0 | 1.70318 | 3.03718 | 0 | −5.48274 | ||||||||||||||||||
1.11 | −0.738482 | 0 | −1.45464 | −3.79116 | 0 | 4.03115 | 2.55119 | 0 | 2.79970 | ||||||||||||||||||
1.12 | −0.477293 | 0 | −1.77219 | 0.869095 | 0 | 5.04945 | 1.80044 | 0 | −0.414813 | ||||||||||||||||||
1.13 | −0.342177 | 0 | −1.88292 | −4.14215 | 0 | −0.810419 | 1.32864 | 0 | 1.41735 | ||||||||||||||||||
1.14 | 0.328801 | 0 | −1.89189 | 3.16539 | 0 | −3.22876 | −1.27966 | 0 | 1.04078 | ||||||||||||||||||
1.15 | 0.349081 | 0 | −1.87814 | −1.36534 | 0 | −0.0430977 | −1.35379 | 0 | −0.476616 | ||||||||||||||||||
1.16 | 0.425199 | 0 | −1.81921 | 3.04539 | 0 | 0.946556 | −1.62392 | 0 | 1.29490 | ||||||||||||||||||
1.17 | 0.462244 | 0 | −1.78633 | −1.15565 | 0 | −1.19216 | −1.75021 | 0 | −0.534193 | ||||||||||||||||||
1.18 | 1.28997 | 0 | −0.335977 | −3.81229 | 0 | 4.19464 | −3.01334 | 0 | −4.91774 | ||||||||||||||||||
1.19 | 1.43135 | 0 | 0.0487521 | −1.62138 | 0 | 3.43484 | −2.79291 | 0 | −2.32076 | ||||||||||||||||||
1.20 | 1.44158 | 0 | 0.0781455 | −1.16845 | 0 | −5.22170 | −2.77050 | 0 | −1.68442 | ||||||||||||||||||
See all 26 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(-1\) |
\(503\) | \(1\) |
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 | 4527.2.a.o | 26 | |
3.b | odd | 2 | 1 | 503.2.a.f | ✓ | 26 | |
12.b | even | 2 | 1 | 8048.2.a.u | 26 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
503.2.a.f | ✓ | 26 | 3.b | odd | 2 | 1 | |
4527.2.a.o | 26 | 1.a | even | 1 | 1 | trivial | |
8048.2.a.u | 26 | 12.b | even | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4527))\):
\( T_{2}^{26} + 4 T_{2}^{25} - 36 T_{2}^{24} - 154 T_{2}^{23} + 554 T_{2}^{22} + 2577 T_{2}^{21} - 4772 T_{2}^{20} - 24652 T_{2}^{19} + 25321 T_{2}^{18} + 149131 T_{2}^{17} - 86017 T_{2}^{16} - 595540 T_{2}^{15} + 189834 T_{2}^{14} + \cdots - 1583 \) |
\( T_{5}^{26} + 9 T_{5}^{25} - 71 T_{5}^{24} - 873 T_{5}^{23} + 1333 T_{5}^{22} + 35769 T_{5}^{21} + 27305 T_{5}^{20} - 795330 T_{5}^{19} - 1730386 T_{5}^{18} + 10082887 T_{5}^{17} + 35969747 T_{5}^{16} + \cdots + 7351042048 \) |
\( T_{7}^{26} - 11 T_{7}^{25} - 63 T_{7}^{24} + 1107 T_{7}^{23} + 43 T_{7}^{22} - 44446 T_{7}^{21} + 93217 T_{7}^{20} + 898238 T_{7}^{19} - 3273637 T_{7}^{18} - 9066021 T_{7}^{17} + 53508259 T_{7}^{16} + \cdots + 5803441 \) |