Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, 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("8023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8023.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: | \(64.0639775417\) |
Analytic rank: | \(1\) |
Dimension: | \(158\) |
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 | −2.79904 | −0.951830 | 5.83462 | 2.72456 | 2.66421 | 1.55879 | −10.7333 | −2.09402 | −7.62616 | ||||||||||||||||||
1.2 | −2.78025 | −2.83508 | 5.72982 | −1.35792 | 7.88223 | 4.56765 | −10.3698 | 5.03765 | 3.77538 | ||||||||||||||||||
1.3 | −2.75717 | −0.782411 | 5.60200 | −3.11881 | 2.15724 | 0.297168 | −9.93135 | −2.38783 | 8.59909 | ||||||||||||||||||
1.4 | −2.74732 | 2.10960 | 5.54775 | 3.39073 | −5.79574 | −0.0705501 | −9.74679 | 1.45041 | −9.31541 | ||||||||||||||||||
1.5 | −2.74512 | 2.49890 | 5.53568 | 0.133996 | −6.85979 | 0.778013 | −9.70588 | 3.24451 | −0.367836 | ||||||||||||||||||
1.6 | −2.73131 | −2.15430 | 5.46003 | −2.36711 | 5.88407 | −3.03890 | −9.45041 | 1.64103 | 6.46530 | ||||||||||||||||||
1.7 | −2.70862 | 0.748763 | 5.33660 | −3.98594 | −2.02811 | 0.912141 | −9.03756 | −2.43935 | 10.7964 | ||||||||||||||||||
1.8 | −2.70672 | −0.0191468 | 5.32634 | 0.870977 | 0.0518250 | −3.03945 | −9.00349 | −2.99963 | −2.35749 | ||||||||||||||||||
1.9 | −2.67852 | 0.688962 | 5.17445 | −3.33373 | −1.84540 | 3.78681 | −8.50280 | −2.52533 | 8.92945 | ||||||||||||||||||
1.10 | −2.65311 | 3.18762 | 5.03901 | 1.63340 | −8.45712 | −4.20358 | −8.06283 | 7.16092 | −4.33359 | ||||||||||||||||||
1.11 | −2.60210 | −3.36394 | 4.77094 | 3.49358 | 8.75331 | 4.61670 | −7.21028 | 8.31606 | −9.09066 | ||||||||||||||||||
1.12 | −2.54938 | 0.0117245 | 4.49933 | 3.26987 | −0.0298901 | −0.929031 | −6.37175 | −2.99986 | −8.33615 | ||||||||||||||||||
1.13 | −2.54054 | 2.90668 | 4.45432 | −2.39844 | −7.38453 | 0.864832 | −6.23529 | 5.44881 | 6.09333 | ||||||||||||||||||
1.14 | −2.51950 | −2.51323 | 4.34790 | 1.49157 | 6.33210 | −1.81281 | −5.91556 | 3.31634 | −3.75802 | ||||||||||||||||||
1.15 | −2.49733 | −3.32636 | 4.23663 | −4.15753 | 8.30700 | −2.74619 | −5.58560 | 8.06465 | 10.3827 | ||||||||||||||||||
1.16 | −2.47274 | −2.32483 | 4.11444 | −0.448444 | 5.74869 | 4.71625 | −5.22846 | 2.40481 | 1.10889 | ||||||||||||||||||
1.17 | −2.44908 | −0.864554 | 3.99799 | 2.08542 | 2.11736 | −1.35512 | −4.89325 | −2.25255 | −5.10735 | ||||||||||||||||||
1.18 | −2.43745 | −0.327529 | 3.94116 | −2.07610 | 0.798335 | −0.184041 | −4.73147 | −2.89272 | 5.06038 | ||||||||||||||||||
1.19 | −2.36796 | 1.87225 | 3.60725 | 0.382969 | −4.43341 | 2.54225 | −3.80591 | 0.505313 | −0.906856 | ||||||||||||||||||
1.20 | −2.36619 | −2.12839 | 3.59886 | 0.442767 | 5.03618 | −4.08071 | −3.78320 | 1.53005 | −1.04767 | ||||||||||||||||||
See next 80 embeddings (of 158 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(71\) | \(1\) |
\(113\) | \(1\) |
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 | 8023.2.a.c | ✓ | 158 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8023.2.a.c | ✓ | 158 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{158} + 24 T_{2}^{157} + 51 T_{2}^{156} - 3329 T_{2}^{155} - 25618 T_{2}^{154} + 183204 T_{2}^{153} + \cdots + 928013 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8023))\).