Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [95,11,Mod(21,95)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(95, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("95.21");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 95 = 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 95.n (of order \(18\), degree \(6\), 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: | \(60.3589390040\) |
Analytic rank: | \(0\) |
Dimension: | \(396\) |
Relative dimension: | \(66\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
21.1 | −61.1091 | − | 10.7752i | 90.6903 | − | 108.081i | 2655.97 | + | 966.695i | −1313.26 | + | 477.988i | −6706.59 | + | 5627.50i | 1391.50 | + | 2410.15i | −96859.5 | − | 55921.9i | 6797.09 | + | 38548.2i | 85402.6 | − | 15058.8i |
21.2 | −59.5178 | − | 10.4946i | −238.205 | + | 283.882i | 2469.99 | + | 899.002i | 1313.26 | − | 477.988i | 17156.7 | − | 14396.1i | 3332.39 | + | 5771.87i | −83978.3 | − | 48484.9i | −13593.4 | − | 77092.1i | −83178.7 | + | 14666.6i |
21.3 | −57.7744 | − | 10.1872i | 6.52713 | − | 7.77873i | 2271.86 | + | 826.889i | 1313.26 | − | 477.988i | −456.345 | + | 382.919i | −4938.84 | − | 8554.32i | −70806.3 | − | 40880.1i | 10235.8 | + | 58050.4i | −80742.2 | + | 14237.0i |
21.4 | −57.3380 | − | 10.1102i | −246.025 | + | 293.202i | 2223.18 | + | 809.171i | −1313.26 | + | 477.988i | 17070.9 | − | 14324.2i | −3262.03 | − | 5650.01i | −67659.4 | − | 39063.2i | −15185.0 | − | 86118.3i | 80132.2 | − | 14129.5i |
21.5 | −56.2513 | − | 9.91861i | 283.038 | − | 337.311i | 2103.58 | + | 765.641i | 1313.26 | − | 477.988i | −19266.9 | + | 16166.8i | −8601.00 | − | 14897.4i | −60081.2 | − | 34687.9i | −23414.7 | − | 132791.i | −78613.5 | + | 13861.7i |
21.6 | −55.8946 | − | 9.85573i | −94.5815 | + | 112.718i | 2064.83 | + | 751.535i | −1313.26 | + | 477.988i | 6397.51 | − | 5368.15i | 7163.28 | + | 12407.2i | −57673.1 | − | 33297.6i | 6494.10 | + | 36829.9i | 78115.1 | − | 13773.8i |
21.7 | −51.6407 | − | 9.10564i | 231.862 | − | 276.323i | 1621.60 | + | 590.214i | −1313.26 | + | 477.988i | −14489.6 | + | 12158.2i | −4425.19 | − | 7664.65i | −31864.3 | − | 18396.9i | −12340.4 | − | 69985.7i | 72170.0 | − | 12725.5i |
21.8 | −50.8093 | − | 8.95904i | −106.608 | + | 127.051i | 1539.07 | + | 560.176i | 1313.26 | − | 477.988i | 6554.95 | − | 5500.26i | 12381.7 | + | 21445.8i | −27427.2 | − | 15835.1i | 5477.15 | + | 31062.5i | −71008.1 | + | 12520.6i |
21.9 | −49.0540 | − | 8.64954i | 84.6169 | − | 100.843i | 1369.23 | + | 498.360i | −1313.26 | + | 477.988i | −5023.04 | + | 4214.83i | −12628.7 | − | 21873.6i | −18683.1 | − | 10786.7i | 7244.56 | + | 41085.9i | 68555.0 | − | 12088.1i |
21.10 | −47.5593 | − | 8.38598i | 230.589 | − | 274.806i | 1229.31 | + | 447.434i | −1313.26 | + | 477.988i | −13271.2 | + | 11135.8i | 14205.4 | + | 24604.4i | −11886.4 | − | 6862.64i | −12093.0 | − | 68582.6i | 66466.1 | − | 11719.8i |
21.11 | −45.6687 | − | 8.05262i | 180.078 | − | 214.608i | 1058.54 | + | 385.276i | 1313.26 | − | 477.988i | −9952.08 | + | 8350.78i | 14827.6 | + | 25682.2i | −4115.32 | − | 2375.98i | −3374.99 | − | 19140.5i | −63823.9 | + | 11253.9i |
21.12 | −44.4252 | − | 7.83336i | 52.7241 | − | 62.8342i | 949.993 | + | 345.769i | 1313.26 | − | 477.988i | −2834.48 | + | 2378.41i | −3796.41 | − | 6575.58i | 509.392 | + | 294.098i | 9085.45 | + | 51526.2i | −62086.1 | + | 10947.5i |
21.13 | −42.7196 | − | 7.53262i | 216.249 | − | 257.716i | 805.978 | + | 293.352i | 1313.26 | − | 477.988i | −11179.3 | + | 9380.59i | 1612.29 | + | 2792.57i | 6247.25 | + | 3606.85i | −9399.94 | − | 53309.7i | −59702.4 | + | 10527.2i |
21.14 | −42.3555 | − | 7.46841i | −264.359 | + | 315.050i | 775.963 | + | 282.427i | −1313.26 | + | 477.988i | 13550.0 | − | 11369.8i | −2364.23 | − | 4094.96i | 7383.72 | + | 4262.99i | −19117.5 | − | 108421.i | 59193.6 | − | 10437.4i |
21.15 | −40.9201 | − | 7.21531i | −230.168 | + | 274.304i | 660.147 | + | 240.274i | 1313.26 | − | 477.988i | 11397.7 | − | 9563.80i | −2238.39 | − | 3877.00i | 11568.5 | + | 6679.10i | −12011.4 | − | 68120.1i | −57187.5 | + | 10083.7i |
21.16 | −40.1539 | − | 7.08022i | −57.0549 | + | 67.9954i | 599.962 | + | 218.368i | −1313.26 | + | 477.988i | 2772.40 | − | 2326.32i | 3046.11 | + | 5276.02i | 13613.5 | + | 7859.76i | 8885.64 | + | 50393.0i | 56116.8 | − | 9894.90i |
21.17 | −37.5879 | − | 6.62777i | −167.186 | + | 199.244i | 406.681 | + | 148.020i | 1313.26 | − | 477.988i | 7604.72 | − | 6381.11i | −12140.7 | − | 21028.2i | 19542.3 | + | 11282.8i | −1493.44 | − | 8469.71i | −52530.8 | + | 9262.59i |
21.18 | −30.0368 | − | 5.29630i | 85.7905 | − | 102.241i | −88.0867 | − | 32.0609i | −1313.26 | + | 477.988i | −3118.37 | + | 2616.63i | −360.285 | − | 624.031i | 29523.9 | + | 17045.6i | 7160.51 | + | 40609.3i | 41977.7 | − | 7401.80i |
21.19 | −27.5211 | − | 4.85272i | −183.416 | + | 218.587i | −228.382 | − | 83.1241i | −1313.26 | + | 477.988i | 6108.56 | − | 5125.69i | −4255.32 | − | 7370.44i | 30664.5 | + | 17704.1i | −3884.98 | − | 22032.8i | 38461.9 | − | 6781.88i |
21.20 | −23.9059 | − | 4.21526i | 25.9976 | − | 30.9827i | −408.520 | − | 148.689i | 1313.26 | − | 477.988i | −752.096 | + | 631.084i | 8280.45 | + | 14342.2i | 30666.4 | + | 17705.2i | 9969.70 | + | 56541.0i | −33409.6 | + | 5891.01i |
See next 80 embeddings (of 396 total) |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
19.f | odd | 18 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 95.11.n.a | ✓ | 396 |
19.f | odd | 18 | 1 | inner | 95.11.n.a | ✓ | 396 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
95.11.n.a | ✓ | 396 | 1.a | even | 1 | 1 | trivial |
95.11.n.a | ✓ | 396 | 19.f | odd | 18 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{11}^{\mathrm{new}}(95, [\chi])\).