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Properties

Label 35.10.b.a
Level $35$
Weight $10$
Character orbit 35.b
Analytic conductor $18.026$
Analytic rank $0$
Dimension $26$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,10,Mod(29,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.29");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 35.b (of order \(2\), degree \(1\), 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: \(26\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 26 q - 5460 q^{4} - 1714 q^{5} + 6156 q^{6} - 185446 q^{9} + 70264 q^{10} - 132540 q^{11} + 153664 q^{14} + 603128 q^{15} - 888268 q^{16} + 1380456 q^{19} + 5139308 q^{20} - 758716 q^{21} - 3568824 q^{24}+ \cdots - 743625048 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
29.1 − 41.1148i 238.422i −1178.43 −1364.57 − 301.785i 9802.66 2401.00i 27400.1i −37161.8 −12407.8 + 56104.1i
29.2 − 39.5568i − 124.465i −1052.74 −391.953 + 1341.45i −4923.44 2401.00i 21389.9i 4191.43 53063.6 + 15504.4i
29.3 − 36.3540i − 180.517i −809.610 −1083.80 − 882.324i −6562.51 − 2401.00i 10819.3i −12903.4 −32076.0 + 39400.5i
29.4 − 34.7267i 125.299i −693.945 182.264 + 1385.61i 4351.22 − 2401.00i 6318.35i 3983.15 48117.6 − 6329.44i
29.5 − 27.4175i − 243.480i −239.721 1314.36 − 474.963i −6675.61 2401.00i − 7465.23i −39599.4 −13022.3 − 36036.4i
29.6 − 25.4620i 111.752i −136.314 −1350.26 − 360.442i 2845.44 − 2401.00i − 9565.72i 7194.45 −9177.58 + 34380.4i
29.7 − 24.6718i 212.283i −96.6987 1243.25 + 638.325i 5237.41 2401.00i − 10246.2i −25381.1 15748.6 − 30673.2i
29.8 − 24.6549i 17.6734i −95.8645 −12.5812 − 1397.49i 435.737 2401.00i − 10259.8i 19370.6 −34454.9 + 310.189i
29.9 − 21.7968i − 114.276i 36.8999 1092.36 + 871.709i −2490.84 − 2401.00i − 11964.3i 6624.06 19000.4 − 23809.9i
29.10 − 16.1576i − 17.2974i 250.933 −1196.41 + 722.315i −279.484 2401.00i − 12327.1i 19383.8 11670.9 + 19331.0i
29.11 − 13.6862i 223.464i 324.689 603.501 − 1260.52i 3058.37 − 2401.00i − 11451.1i −30253.3 −17251.7 − 8259.61i
29.12 − 7.74202i − 216.721i 452.061 −1016.98 + 958.582i −1677.86 − 2401.00i − 7463.78i −27284.9 7421.36 + 7873.47i
29.13 − 1.80576i − 23.8664i 508.739 1123.82 − 830.751i −43.0971 − 2401.00i − 1843.21i 19113.4 −1500.14 − 2029.36i
29.14 1.80576i 23.8664i 508.739 1123.82 + 830.751i −43.0971 2401.00i 1843.21i 19113.4 −1500.14 + 2029.36i
29.15 7.74202i 216.721i 452.061 −1016.98 − 958.582i −1677.86 2401.00i 7463.78i −27284.9 7421.36 − 7873.47i
29.16 13.6862i − 223.464i 324.689 603.501 + 1260.52i 3058.37 2401.00i 11451.1i −30253.3 −17251.7 + 8259.61i
29.17 16.1576i 17.2974i 250.933 −1196.41 − 722.315i −279.484 − 2401.00i 12327.1i 19383.8 11670.9 − 19331.0i
29.18 21.7968i 114.276i 36.8999 1092.36 − 871.709i −2490.84 2401.00i 11964.3i 6624.06 19000.4 + 23809.9i
29.19 24.6549i − 17.6734i −95.8645 −12.5812 + 1397.49i 435.737 − 2401.00i 10259.8i 19370.6 −34454.9 − 310.189i
29.20 24.6718i − 212.283i −96.6987 1243.25 − 638.325i 5237.41 − 2401.00i 10246.2i −25381.1 15748.6 + 30673.2i
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 29.26
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 35.10.b.a ✓ 26
5.b even 2 1 inner 35.10.b.a ✓ 26
5.c odd 4 1 175.10.a.l 13
5.c odd 4 1 175.10.a.m 13
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
35.10.b.a ✓ 26 1.a even 1 1 trivial
35.10.b.a ✓ 26 5.b even 2 1 inner
175.10.a.l 13 5.c odd 4 1
175.10.a.m 13 5.c odd 4 1

Hecke kernels

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