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Properties

Label 95.5.h.a
Level $95$
Weight $5$
Character orbit 95.h
Analytic conductor $9.820$
Analytic rank $0$
Dimension $76$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,5,Mod(69,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.69");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 95.h (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: \(9.82014649297\)
Analytic rank: \(0\)
Dimension: \(76\)
Relative dimension: \(38\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 76 q - 304 q^{4} + 8 q^{5} + 44 q^{6} - 920 q^{9} - 300 q^{10} - 212 q^{11} + 108 q^{14} + 12 q^{15} - 2068 q^{16} - 184 q^{19} + 108 q^{20} + 1668 q^{21} + 2962 q^{24} - 592 q^{25} - 1348 q^{26} + 1974 q^{29}+ \cdots + 1922 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
69.1 −3.77522 − 6.53887i 6.96380 + 12.0616i −20.5045 + 35.5148i −1.04200 + 24.9783i 52.5797 − 91.0706i − 48.2013i 188.829 −56.4889 + 97.8417i 167.263 − 87.4848i
69.2 −3.76648 − 6.52374i 3.11226 + 5.39059i −20.3728 + 35.2867i 0.802884 − 24.9871i 23.4445 − 40.6071i 75.6044i 186.408 21.1277 − 36.5942i −166.033 + 88.8757i
69.3 −3.64078 − 6.30602i −3.43435 − 5.94847i −18.5106 + 32.0613i 21.9779 + 11.9152i −25.0075 + 43.3142i 17.2327i 153.067 16.9104 − 29.2897i −4.87924 − 181.974i
69.4 −3.54958 − 6.14806i −6.01586 − 10.4198i −17.1991 + 29.7897i −24.2650 + 6.01734i −42.7076 + 73.9716i − 15.4601i 130.611 −31.8810 + 55.2196i 123.126 + 127.824i
69.5 −3.11910 − 5.40243i −2.35284 − 4.07524i −11.4575 + 19.8450i 8.90373 − 23.3607i −14.6775 + 25.4222i − 76.5970i 43.1375 29.4283 − 50.9712i −153.976 + 24.7625i
69.6 −3.00419 − 5.20342i 3.88331 + 6.72609i −10.0504 + 17.4077i −21.8549 − 12.1394i 23.3324 − 40.4129i − 30.4403i 24.6386 10.3398 − 17.9091i 2.49013 + 150.189i
69.7 −2.66296 − 4.61238i 1.85207 + 3.20788i −6.18271 + 10.7088i −14.7427 + 20.1904i 9.86398 − 17.0849i 14.5505i −19.3575 33.6397 − 58.2656i 132.385 + 14.2324i
69.8 −2.59162 − 4.48881i −8.46267 − 14.6578i −5.43295 + 9.41015i 18.4325 − 16.8891i −43.8640 + 75.9747i 55.8877i −26.6112 −102.734 + 177.940i −123.582 − 38.9699i
69.9 −2.46490 − 4.26933i 4.84646 + 8.39432i −4.15145 + 7.19052i 23.9835 + 7.05628i 23.8921 − 41.3823i 69.9627i −37.9452 −6.47639 + 11.2174i −28.9913 − 119.787i
69.10 −2.38931 − 4.13841i 7.89144 + 13.6684i −3.41764 + 5.91952i 19.5580 − 15.5719i 37.7102 − 65.3160i − 37.3600i −43.7948 −84.0496 + 145.578i −111.173 − 43.7332i
69.11 −2.18954 − 3.79239i −1.74795 − 3.02754i −1.58817 + 2.75078i 18.5029 + 16.8120i −7.65442 + 13.2578i − 41.3991i −56.1559 34.3893 − 59.5641i 23.2448 − 106.981i
69.12 −1.92278 − 3.33035i −2.90103 − 5.02473i 0.605829 − 1.04933i −21.7327 − 12.3567i −11.1561 + 19.3229i 80.9610i −66.1885 23.6681 − 40.9943i 0.635089 + 96.1369i
69.13 −1.67979 − 2.90949i −7.21014 − 12.4883i 2.35658 − 4.08172i −1.56715 + 24.9508i −24.2231 + 41.9556i − 1.10616i −69.5877 −63.4722 + 109.937i 75.2267 − 37.3526i
69.14 −1.11418 − 1.92982i −1.03164 − 1.78686i 5.51719 − 9.55605i 13.1047 − 21.2901i −2.29888 + 3.98178i 5.41425i −60.2425 38.3714 − 66.4613i −55.6871 − 1.56873i
69.15 −1.05148 − 1.82122i 5.77301 + 9.99914i 5.78877 − 10.0264i −18.0468 − 17.3007i 12.1404 − 21.0279i − 26.6350i −57.9946 −26.1553 + 45.3022i −12.5325 + 51.0586i
69.16 −1.01799 − 1.76321i −6.41362 − 11.1087i 5.92739 − 10.2665i −20.4757 − 14.3439i −13.0580 + 22.6171i − 78.3466i −56.7118 −41.7691 + 72.3462i −4.44726 + 50.7049i
69.17 −0.758009 − 1.31291i 7.17678 + 12.4306i 6.85085 − 11.8660i −13.0699 + 21.3115i 10.8801 − 18.8449i 45.9657i −45.0283 −62.5124 + 108.275i 37.8871 + 1.00530i
69.18 −0.275605 − 0.477362i 4.15531 + 7.19720i 7.84808 − 13.5933i 12.3494 + 21.7369i 2.29045 − 3.96717i − 93.5433i −17.4712 5.96685 − 10.3349i 6.97282 − 11.8859i
69.19 −0.116045 − 0.200997i −2.09799 − 3.63383i 7.97307 − 13.8098i −17.7122 + 17.6430i −0.486925 + 0.843379i − 17.0392i −7.41441 31.6968 − 54.9005i 5.60161 + 1.51270i
69.20 0.116045 + 0.200997i 2.09799 + 3.63383i 7.97307 − 13.8098i 24.1354 − 6.51771i −0.486925 + 0.843379i 17.0392i 7.41441 31.6968 − 54.9005i 4.11084 + 4.09479i
See all 76 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 69.38
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
19.d odd 6 1 inner
95.h odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.5.h.a ✓ 76
5.b even 2 1 inner 95.5.h.a ✓ 76
19.d odd 6 1 inner 95.5.h.a ✓ 76
95.h odd 6 1 inner 95.5.h.a ✓ 76
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.5.h.a ✓ 76 1.a even 1 1 trivial
95.5.h.a ✓ 76 5.b even 2 1 inner
95.5.h.a ✓ 76 19.d odd 6 1 inner
95.5.h.a ✓ 76 95.h odd 6 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(95, [\chi])\).