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Properties

Label 35.10.j.a
Level $35$
Weight $10$
Character orbit 35.j
Analytic conductor $18.026$
Analytic rank $0$
Dimension $68$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,10,Mod(4,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.4");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 35.j (of order \(6\), degree \(2\), 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: \(18.0262542657\)
Analytic rank: \(0\)
Dimension: \(68\)
Relative dimension: \(34\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 68 q + 8190 q^{4} + 283 q^{5} + 3768 q^{6} + 212878 q^{9} - 35564 q^{10} + 20580 q^{11} + 245558 q^{14} - 251762 q^{15} - 1565382 q^{16} + 1617200 q^{19} + 384184 q^{20} - 392432 q^{21} + 1749444 q^{24}+ \cdots + 3178969668 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
4.1 −36.5251 + 21.0878i 102.116 + 58.9569i 633.390 − 1097.06i −1329.14 − 431.869i −4973.09 −5598.79 − 3001.19i 31833.3i −2889.66 − 5005.04i 57654.2 − 12254.6i
4.2 −35.8858 + 20.7187i −184.448 − 106.491i 602.527 − 1043.61i 1390.19 − 143.200i 8825.40 −4378.93 − 4602.02i 28718.3i 12839.1 + 22238.0i −46921.0 + 33941.7i
4.3 −35.3468 + 20.4075i 43.4263 + 25.0722i 576.931 − 999.273i 387.775 + 1342.67i −2046.64 4188.72 + 4775.79i 26197.5i −8584.27 − 14868.4i −41107.1 − 39545.5i
4.4 −32.3116 + 18.6551i −168.242 − 97.1346i 440.026 − 762.147i −1358.14 + 329.525i 7248.23 1751.31 + 6106.27i 13732.1i 9028.78 + 15638.3i 37736.3 − 35983.7i
4.5 −30.6738 + 17.7095i 0.297969 + 0.172033i 371.254 − 643.031i 442.043 − 1325.79i −12.1865 5985.24 − 2128.50i 8164.37i −9841.44 − 17045.9i 9919.98 + 48495.4i
4.6 −27.8265 + 16.0657i 156.189 + 90.1756i 260.211 − 450.698i 887.615 + 1079.47i −5794.92 −3258.53 − 5453.04i 270.581i 6421.77 + 11122.8i −42041.7 − 15777.9i
4.7 −27.6841 + 15.9834i 230.747 + 133.222i 254.940 − 441.569i 776.768 − 1161.79i −8517.36 42.1213 + 6352.31i − 67.7831i 25654.5 + 44435.0i −2934.76 + 44578.5i
4.8 −22.4039 + 12.9349i −81.7829 − 47.2174i 78.6223 − 136.178i −750.881 − 1178.69i 2443.00 −5976.81 + 2152.05i − 9177.44i −5382.54 − 9322.83i 32068.8 + 16694.6i
4.9 −21.6431 + 12.4956i −124.860 − 72.0879i 56.2825 − 97.4842i −505.151 + 1303.05i 3603.14 1540.11 − 6162.93i − 9982.40i 551.823 + 955.786i −5349.45 − 34514.3i
4.10 −20.6049 + 11.8963i −52.9576 − 30.5751i 27.0421 − 46.8384i 1394.21 + 96.5081i 1454.92 −4324.08 + 4653.59i − 10895.0i −7971.83 − 13807.6i −29875.6 + 14597.3i
4.11 −17.7536 + 10.2500i 138.618 + 80.0311i −45.8742 + 79.4564i −1388.74 − 156.575i −3281.28 5604.70 − 2990.15i − 12376.9i 2968.46 + 5141.53i 26260.0 − 11454.9i
4.12 −14.7876 + 8.53763i 107.686 + 62.1724i −110.218 + 190.903i −936.651 + 1037.21i −2123.22 −3129.65 + 5528.01i − 12506.5i −2110.69 − 3655.82i 4995.50 − 23334.7i
4.13 −12.6515 + 7.30432i −237.207 − 136.952i −149.294 + 258.585i 343.475 − 1354.68i 4001.35 6124.66 + 1685.86i − 11841.6i 27670.0 + 47925.9i 5549.54 + 19647.5i
4.14 −8.03642 + 4.63983i −42.5238 − 24.5511i −212.944 + 368.830i 1267.36 + 589.003i 455.652 6091.79 + 1801.04i − 8703.28i −8635.99 − 14958.0i −12917.9 + 1146.86i
4.15 −6.57154 + 3.79408i 105.463 + 60.8890i −227.210 + 393.539i 1041.64 − 931.723i −924.071 −3603.23 − 5231.67i − 7333.35i −2426.56 − 4202.92i −3310.15 + 10074.9i
4.16 −2.09289 + 1.20833i −91.4053 − 52.7729i −253.080 + 438.347i −1104.79 − 855.896i 255.068 −1695.36 − 6122.04i − 2460.55i −4271.55 − 7398.54i 3346.41 + 456.340i
4.17 −1.15888 + 0.669077i −212.277 − 122.558i −255.105 + 441.854i 563.506 + 1278.90i 328.003 −6227.19 + 1255.26i − 1367.87i 20199.5 + 34986.6i −1508.72 − 1105.06i
4.18 1.15888 − 0.669077i 212.277 + 122.558i −255.105 + 441.854i 825.807 + 1127.46i 328.003 6227.19 − 1255.26i 1367.87i 20199.5 + 34986.6i 1711.37 + 754.058i
4.19 2.09289 − 1.20833i 91.4053 + 52.7729i −253.080 + 438.347i −188.831 − 1384.73i 255.068 1695.36 + 6122.04i 2460.55i −4271.55 − 7398.54i −2068.41 − 2669.91i
4.20 6.57154 − 3.79408i −105.463 − 60.8890i −227.210 + 393.539i −1327.72 + 436.226i −924.071 3603.23 + 5231.67i 7333.35i −2426.56 − 4202.92i −7070.06 + 7904.14i
See all 68 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 4.34
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
7.c even 3 1 inner
35.j even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 35.10.j.a ✓ 68
5.b even 2 1 inner 35.10.j.a ✓ 68
7.c even 3 1 inner 35.10.j.a ✓ 68
35.j even 6 1 inner 35.10.j.a ✓ 68
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
35.10.j.a ✓ 68 1.a even 1 1 trivial
35.10.j.a ✓ 68 5.b even 2 1 inner
35.10.j.a ✓ 68 7.c even 3 1 inner
35.10.j.a ✓ 68 35.j even 6 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{10}^{\mathrm{new}}(35, [\chi])\).