Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.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: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(29\) |
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 | −2.76452 | 1.00000 | 5.64259 | 4.23744 | −2.76452 | −1.00000 | −10.0700 | 1.00000 | −11.7145 | ||||||||||||||||||
1.2 | −2.55639 | 1.00000 | 4.53513 | 0.170446 | −2.55639 | −1.00000 | −6.48077 | 1.00000 | −0.435725 | ||||||||||||||||||
1.3 | −2.32184 | 1.00000 | 3.39092 | 1.73819 | −2.32184 | −1.00000 | −3.22949 | 1.00000 | −4.03578 | ||||||||||||||||||
1.4 | −2.24191 | 1.00000 | 3.02615 | −1.20404 | −2.24191 | −1.00000 | −2.30052 | 1.00000 | 2.69935 | ||||||||||||||||||
1.5 | −2.08804 | 1.00000 | 2.35993 | −2.57813 | −2.08804 | −1.00000 | −0.751541 | 1.00000 | 5.38324 | ||||||||||||||||||
1.6 | −2.00218 | 1.00000 | 2.00873 | −0.971545 | −2.00218 | −1.00000 | −0.0174879 | 1.00000 | 1.94521 | ||||||||||||||||||
1.7 | −1.96996 | 1.00000 | 1.88076 | 4.31773 | −1.96996 | −1.00000 | 0.234907 | 1.00000 | −8.50578 | ||||||||||||||||||
1.8 | −1.47855 | 1.00000 | 0.186109 | 3.98947 | −1.47855 | −1.00000 | 2.68193 | 1.00000 | −5.89863 | ||||||||||||||||||
1.9 | −1.16967 | 1.00000 | −0.631883 | 0.467682 | −1.16967 | −1.00000 | 3.07842 | 1.00000 | −0.547032 | ||||||||||||||||||
1.10 | −0.657179 | 1.00000 | −1.56812 | 0.753891 | −0.657179 | −1.00000 | 2.34489 | 1.00000 | −0.495441 | ||||||||||||||||||
1.11 | −0.630217 | 1.00000 | −1.60283 | −2.79883 | −0.630217 | −1.00000 | 2.27056 | 1.00000 | 1.76387 | ||||||||||||||||||
1.12 | −0.359948 | 1.00000 | −1.87044 | −1.76526 | −0.359948 | −1.00000 | 1.39316 | 1.00000 | 0.635404 | ||||||||||||||||||
1.13 | −0.223362 | 1.00000 | −1.95011 | 1.64565 | −0.223362 | −1.00000 | 0.882304 | 1.00000 | −0.367576 | ||||||||||||||||||
1.14 | −0.220924 | 1.00000 | −1.95119 | 3.22358 | −0.220924 | −1.00000 | 0.872912 | 1.00000 | −0.712166 | ||||||||||||||||||
1.15 | 0.336232 | 1.00000 | −1.88695 | 4.17128 | 0.336232 | −1.00000 | −1.30692 | 1.00000 | 1.40252 | ||||||||||||||||||
1.16 | 0.797866 | 1.00000 | −1.36341 | 0.229986 | 0.797866 | −1.00000 | −2.68355 | 1.00000 | 0.183498 | ||||||||||||||||||
1.17 | 0.830058 | 1.00000 | −1.31100 | −1.52882 | 0.830058 | −1.00000 | −2.74832 | 1.00000 | −1.26901 | ||||||||||||||||||
1.18 | 1.15914 | 1.00000 | −0.656403 | −3.68396 | 1.15914 | −1.00000 | −3.07913 | 1.00000 | −4.27022 | ||||||||||||||||||
1.19 | 1.18058 | 1.00000 | −0.606227 | 0.961582 | 1.18058 | −1.00000 | −3.07686 | 1.00000 | 1.13523 | ||||||||||||||||||
1.20 | 1.22787 | 1.00000 | −0.492335 | 2.78453 | 1.22787 | −1.00000 | −3.06026 | 1.00000 | 3.41904 | ||||||||||||||||||
See all 29 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(-1\) |
\(7\) | \(1\) |
\(191\) | \(1\) |
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 | 4011.2.a.m | ✓ | 29 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
4011.2.a.m | ✓ | 29 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{29} - 6 T_{2}^{28} - 31 T_{2}^{27} + 245 T_{2}^{26} + 318 T_{2}^{25} - 4363 T_{2}^{24} + \cdots - 2816 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4011))\).