Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [11,14,Mod(3,11)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("11.3");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 11 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 11.c (of order \(5\), degree \(4\), minimal) |
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: | no |
Analytic conductor: | \(11.7954021847\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3.1 | −133.057 | + | 96.6717i | −300.655 | − | 925.320i | 5827.33 | − | 17934.7i | 6362.73 | + | 4622.79i | 129456. | + | 94055.7i | −62415.4 | + | 192095.i | 542063. | + | 1.66830e6i | 524011. | − | 380716.i | −1.29350e6 | ||
3.2 | −101.017 | + | 73.3929i | 277.356 | + | 853.615i | 2286.38 | − | 7036.76i | 21001.8 | + | 15258.7i | −90666.9 | − | 65873.3i | 183952. | − | 566147.i | −30602.4 | − | 94184.4i | 638103. | − | 463609.i | −3.24141e6 | ||
3.3 | −97.9783 | + | 71.1854i | 552.972 | + | 1701.87i | 2000.91 | − | 6158.18i | −26557.7 | − | 19295.3i | −175328. | − | 127383.i | −163681. | + | 503758.i | −64254.1 | − | 197754.i | −1.30076e6 | + | 945060.i | 3.97562e6 | ||
3.4 | −64.6899 | + | 46.9999i | −352.519 | − | 1084.94i | −555.683 | + | 1710.22i | −37053.3 | − | 26920.8i | 73796.5 | + | 53616.3i | 24379.1 | − | 75031.2i | −246852. | − | 759732.i | 237007. | − | 172195.i | 3.66225e6 | ||
3.5 | −38.1571 | + | 27.7228i | −502.353 | − | 1546.08i | −1844.05 | + | 5675.41i | 29618.8 | + | 21519.3i | 62030.1 | + | 45067.5i | −28662.8 | + | 88215.0i | −206371. | − | 635143.i | −848181. | + | 616240.i | −1.72674e6 | ||
3.6 | −16.5754 | + | 12.0428i | 423.594 | + | 1303.69i | −2401.75 | + | 7391.83i | 31221.5 | + | 22683.7i | −22721.3 | − | 16508.0i | −38277.0 | + | 117804.i | −101074. | − | 311073.i | −230340. | + | 167352.i | −790684. | ||
3.7 | 19.9401 | − | 14.4873i | 214.083 | + | 658.880i | −2343.74 | + | 7213.30i | −38433.9 | − | 27923.9i | 13814.3 | + | 10036.6i | 86353.5 | − | 265769.i | 120161. | + | 369817.i | 901543. | − | 655009.i | −1.17092e6 | ||
3.8 | 55.3587 | − | 40.2205i | −140.614 | − | 432.765i | −1084.57 | + | 3337.95i | 7579.93 | + | 5507.14i | −25190.2 | − | 18301.8i | −99964.7 | + | 307660.i | 247435. | + | 761526.i | 1.12232e6 | − | 815414.i | 641115. | ||
3.9 | 80.7641 | − | 58.6786i | −728.875 | − | 2243.25i | 548.202 | − | 1687.19i | −12915.0 | − | 9383.32i | −190497. | − | 138404.i | 94448.4 | − | 290682.i | 197989. | + | 609348.i | −3.21106e6 | + | 2.33297e6i | −1.59367e6 | ||
3.10 | 96.0816 | − | 69.8074i | 738.641 | + | 2273.30i | 1827.14 | − | 5623.35i | −7207.48 | − | 5236.54i | 229663. | + | 166860.i | −816.456 | + | 2512.79i | 83648.5 | + | 257444.i | −3.33248e6 | + | 2.42119e6i | −1.05806e6 | ||
3.11 | 112.273 | − | 81.5711i | 22.6986 | + | 69.8590i | 3419.92 | − | 10525.4i | 39045.2 | + | 28368.0i | 8246.91 | + | 5991.73i | 128438. | − | 395292.i | −123297. | − | 379468.i | 1.28547e6 | − | 933948.i | 6.69773e6 | ||
3.12 | 137.025 | − | 99.5545i | −84.9208 | − | 261.359i | 6333.29 | − | 19491.9i | −37394.7 | − | 27168.8i | −37655.8 | − | 27358.5i | −156206. | + | 480753.i | −643923. | − | 1.98179e6i | 1.22874e6 | − | 892730.i | −7.82879e6 | ||
4.1 | −133.057 | − | 96.6717i | −300.655 | + | 925.320i | 5827.33 | + | 17934.7i | 6362.73 | − | 4622.79i | 129456. | − | 94055.7i | −62415.4 | − | 192095.i | 542063. | − | 1.66830e6i | 524011. | + | 380716.i | −1.29350e6 | ||
4.2 | −101.017 | − | 73.3929i | 277.356 | − | 853.615i | 2286.38 | + | 7036.76i | 21001.8 | − | 15258.7i | −90666.9 | + | 65873.3i | 183952. | + | 566147.i | −30602.4 | + | 94184.4i | 638103. | + | 463609.i | −3.24141e6 | ||
4.3 | −97.9783 | − | 71.1854i | 552.972 | − | 1701.87i | 2000.91 | + | 6158.18i | −26557.7 | + | 19295.3i | −175328. | + | 127383.i | −163681. | − | 503758.i | −64254.1 | + | 197754.i | −1.30076e6 | − | 945060.i | 3.97562e6 | ||
4.4 | −64.6899 | − | 46.9999i | −352.519 | + | 1084.94i | −555.683 | − | 1710.22i | −37053.3 | + | 26920.8i | 73796.5 | − | 53616.3i | 24379.1 | + | 75031.2i | −246852. | + | 759732.i | 237007. | + | 172195.i | 3.66225e6 | ||
4.5 | −38.1571 | − | 27.7228i | −502.353 | + | 1546.08i | −1844.05 | − | 5675.41i | 29618.8 | − | 21519.3i | 62030.1 | − | 45067.5i | −28662.8 | − | 88215.0i | −206371. | + | 635143.i | −848181. | − | 616240.i | −1.72674e6 | ||
4.6 | −16.5754 | − | 12.0428i | 423.594 | − | 1303.69i | −2401.75 | − | 7391.83i | 31221.5 | − | 22683.7i | −22721.3 | + | 16508.0i | −38277.0 | − | 117804.i | −101074. | + | 311073.i | −230340. | − | 167352.i | −790684. | ||
4.7 | 19.9401 | + | 14.4873i | 214.083 | − | 658.880i | −2343.74 | − | 7213.30i | −38433.9 | + | 27923.9i | 13814.3 | − | 10036.6i | 86353.5 | + | 265769.i | 120161. | − | 369817.i | 901543. | + | 655009.i | −1.17092e6 | ||
4.8 | 55.3587 | + | 40.2205i | −140.614 | + | 432.765i | −1084.57 | − | 3337.95i | 7579.93 | − | 5507.14i | −25190.2 | + | 18301.8i | −99964.7 | − | 307660.i | 247435. | − | 761526.i | 1.12232e6 | + | 815414.i | 641115. | ||
See all 48 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
11.c | even | 5 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 11.14.c.a | ✓ | 48 |
11.c | even | 5 | 1 | inner | 11.14.c.a | ✓ | 48 |
11.c | even | 5 | 1 | 121.14.a.h | 24 | ||
11.d | odd | 10 | 1 | 121.14.a.i | 24 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
11.14.c.a | ✓ | 48 | 1.a | even | 1 | 1 | trivial |
11.14.c.a | ✓ | 48 | 11.c | even | 5 | 1 | inner |
121.14.a.h | 24 | 11.c | even | 5 | 1 | ||
121.14.a.i | 24 | 11.d | odd | 10 | 1 |
Hecke kernels
This newform subspace is the entire newspace \(S_{14}^{\mathrm{new}}(11, [\chi])\).