Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
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 | −5.46223 | 9.09504 | 21.8360 | −6.15202 | −49.6792 | 2.59059 | −75.5754 | 55.7197 | 33.6038 | ||||||||||||||||||
1.2 | −5.40604 | −2.51556 | 21.2252 | −3.24888 | 13.5992 | 35.6131 | −71.4960 | −20.6720 | 17.5635 | ||||||||||||||||||
1.3 | −5.33984 | −6.59560 | 20.5139 | 12.0752 | 35.2195 | 18.2315 | −66.8223 | 16.5020 | −64.4799 | ||||||||||||||||||
1.4 | −5.05256 | 9.36203 | 17.5283 | 14.1438 | −47.3022 | −13.7151 | −48.1425 | 60.6475 | −71.4625 | ||||||||||||||||||
1.5 | −4.85844 | −5.73018 | 15.6044 | 14.4569 | 27.8397 | −13.1859 | −36.9457 | 5.83494 | −70.2380 | ||||||||||||||||||
1.6 | −4.80125 | −5.52870 | 15.0520 | 18.8098 | 26.5447 | 0.563586 | −33.8585 | 3.56656 | −90.3106 | ||||||||||||||||||
1.7 | −4.78088 | 1.15757 | 14.8568 | −21.3015 | −5.53419 | 24.0536 | −32.7814 | −25.6600 | 101.840 | ||||||||||||||||||
1.8 | −4.52050 | −1.75128 | 12.4349 | −13.0472 | 7.91667 | 4.32755 | −20.0482 | −23.9330 | 58.9799 | ||||||||||||||||||
1.9 | −3.90499 | 3.52020 | 7.24897 | −10.7056 | −13.7464 | 28.1424 | 2.93275 | −14.6082 | 41.8054 | ||||||||||||||||||
1.10 | −3.81936 | 8.34786 | 6.58755 | 2.56409 | −31.8835 | −3.42361 | 5.39467 | 42.6867 | −9.79321 | ||||||||||||||||||
1.11 | −3.53489 | 7.81725 | 4.49548 | 1.07981 | −27.6332 | −33.3014 | 12.3881 | 34.1094 | −3.81700 | ||||||||||||||||||
1.12 | −3.52844 | −3.06369 | 4.44988 | −14.8551 | 10.8100 | −18.1642 | 12.5264 | −17.6138 | 52.4155 | ||||||||||||||||||
1.13 | −3.43471 | −1.13642 | 3.79726 | −2.82850 | 3.90328 | −33.5669 | 14.4352 | −25.7086 | 9.71508 | ||||||||||||||||||
1.14 | −3.22072 | −8.71909 | 2.37305 | 13.5152 | 28.0818 | −24.0687 | 18.1228 | 49.0226 | −43.5288 | ||||||||||||||||||
1.15 | −3.06679 | −2.01332 | 1.40518 | −11.9365 | 6.17442 | −10.6583 | 20.2249 | −22.9465 | 36.6067 | ||||||||||||||||||
1.16 | −3.04766 | −1.42990 | 1.28824 | 10.9474 | 4.35784 | 8.62569 | 20.4552 | −24.9554 | −33.3638 | ||||||||||||||||||
1.17 | −2.53235 | 8.01322 | −1.58719 | 20.7136 | −20.2923 | 3.06093 | 24.2781 | 37.2117 | −52.4541 | ||||||||||||||||||
1.18 | −2.25115 | 4.02813 | −2.93234 | 4.98765 | −9.06790 | 5.25109 | 24.6103 | −10.7742 | −11.2279 | ||||||||||||||||||
1.19 | −2.06784 | −3.28982 | −3.72402 | 0.905592 | 6.80284 | 0.553732 | 24.2434 | −16.1771 | −1.87262 | ||||||||||||||||||
1.20 | −1.26350 | −9.40007 | −6.40356 | −0.325119 | 11.8770 | −8.80478 | 18.1989 | 61.3613 | 0.410789 | ||||||||||||||||||
See all 50 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(43\) | \(-1\) |
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 | 1849.4.a.i | ✓ | 50 |
43.b | odd | 2 | 1 | 1849.4.a.j | yes | 50 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1849.4.a.i | ✓ | 50 | 1.a | even | 1 | 1 | trivial |
1849.4.a.j | yes | 50 | 43.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{50} + 10 T_{2}^{49} - 243 T_{2}^{48} - 2664 T_{2}^{47} + 26833 T_{2}^{46} + 330340 T_{2}^{45} + \cdots + 16\!\cdots\!28 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1849))\).