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Properties

Label 95.5.n.a
Level $95$
Weight $5$
Character orbit 95.n
Analytic conductor $9.820$
Analytic rank $0$
Dimension $156$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,5,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, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.21");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
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: \(9.82014649297\)
Analytic rank: \(0\)
Dimension: \(156\)
Relative dimension: \(26\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 156 q + 24 q^{3} + 42 q^{4} + 42 q^{6} - 504 q^{9} - 150 q^{10} - 1728 q^{12} - 1122 q^{13} + 576 q^{14} + 2058 q^{16} + 1260 q^{17} + 900 q^{19} + 1026 q^{21} - 4608 q^{22} - 1260 q^{23} - 4032 q^{24}+ \cdots + 28038 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
21.1 −7.46884 − 1.31696i 7.64574 − 9.11184i 39.0141 + 14.2000i −10.5061 + 3.82390i −69.1047 + 57.9857i −3.84130 − 6.65333i −167.601 − 96.7647i −10.5027 − 59.5640i 83.5042 − 14.7240i
21.2 −7.13747 − 1.25853i −7.96405 + 9.49119i 34.3245 + 12.4931i −10.5061 + 3.82390i 68.7881 − 57.7201i −20.4365 − 35.3971i −128.842 − 74.3868i −12.5910 − 71.4072i 79.7993 − 14.0708i
21.3 −6.54219 − 1.15356i −1.35089 + 1.60993i 26.4345 + 9.62136i 10.5061 − 3.82390i 10.6949 − 8.97411i −33.6428 − 58.2711i −69.7908 − 40.2938i 13.2985 + 75.4198i −73.1439 + 12.8972i
21.4 −6.40522 − 1.12941i 5.57742 − 6.64691i 24.7162 + 8.99594i 10.5061 − 3.82390i −43.2317 + 36.2757i 24.7938 + 42.9441i −58.0297 − 33.5035i 0.991699 + 5.62421i −71.6125 + 12.6272i
21.5 −5.10074 − 0.899398i 10.2660 − 12.2346i 10.1735 + 3.70287i 10.5061 − 3.82390i −63.3681 + 53.1722i −34.3114 − 59.4291i 23.2060 + 13.3980i −30.2281 − 171.432i −57.0280 + 10.0556i
21.6 −4.97000 − 0.876344i −5.76535 + 6.87087i 8.89780 + 3.23854i −10.5061 + 3.82390i 34.6750 − 29.0958i 28.6735 + 49.6640i 28.5447 + 16.4803i 0.0958285 + 0.543470i 55.5662 − 9.79783i
21.7 −4.90265 − 0.864470i −10.5069 + 12.5216i 8.25360 + 3.00407i 10.5061 − 3.82390i 62.3362 − 52.3063i −9.68867 − 16.7813i 31.1135 + 17.9634i −32.3309 − 183.357i −54.8133 + 9.66507i
21.8 −4.60373 − 0.811761i 5.16407 − 6.15430i 5.50025 + 2.00193i −10.5061 + 3.82390i −28.7698 + 24.1407i 6.86241 + 11.8860i 41.0786 + 23.7167i 2.85771 + 16.2069i 51.4712 − 9.07576i
21.9 −3.31396 − 0.584341i −4.01758 + 4.78797i −4.39421 − 1.59936i 10.5061 − 3.82390i 16.1119 − 13.5195i 11.0563 + 19.1501i 60.2556 + 34.7886i 7.28183 + 41.2973i −37.0512 + 6.53313i
21.10 −2.49144 − 0.439307i 6.13492 − 7.31131i −9.02082 − 3.28331i 10.5061 − 3.82390i −18.4967 + 15.5206i 46.4921 + 80.5267i 56.0873 + 32.3820i −1.75256 − 9.93925i −27.8551 + 4.91161i
21.11 −1.09522 − 0.193117i −8.57854 + 10.2235i −13.8729 − 5.04931i −10.5061 + 3.82390i 11.3697 − 9.54032i −42.1393 − 72.9874i 29.6287 + 17.1061i −16.8632 − 95.6359i 12.2449 − 2.15911i
21.12 −0.768084 − 0.135434i −2.11315 + 2.51835i −14.4635 − 5.26427i 10.5061 − 3.82390i 1.96415 − 1.64811i −18.0630 − 31.2860i 21.2033 + 12.2417i 12.1888 + 69.1261i −8.58744 + 1.51420i
21.13 −0.654331 − 0.115376i 11.3616 − 13.5403i −14.6202 − 5.32133i −10.5061 + 3.82390i −8.99651 + 7.54897i 5.74665 + 9.95349i 18.1591 + 10.4842i −40.1867 − 227.910i 7.31565 − 1.28995i
21.14 0.0368023 + 0.00648924i −4.11911 + 4.90897i −15.0338 − 5.47184i −10.5061 + 3.82390i −0.183448 + 0.153931i 9.41807 + 16.3126i −1.03558 − 0.597894i 6.93464 + 39.3283i −0.411462 + 0.0725519i
21.15 0.997174 + 0.175829i 2.73108 − 3.25477i −14.0716 − 5.12166i −10.5061 + 3.82390i 3.29564 − 2.76537i 15.5925 + 27.0071i −27.1617 − 15.6818i 10.9307 + 61.9913i −11.1487 + 1.96582i
21.16 2.17727 + 0.383911i 5.55356 − 6.61847i −10.4420 − 3.80057i 10.5061 − 3.82390i 14.6325 − 12.2781i −21.8707 − 37.8811i −51.9104 − 29.9705i 1.10333 + 6.25730i 24.3426 − 4.29225i
21.17 2.97083 + 0.523838i −8.21207 + 9.78677i −6.48365 − 2.35985i 10.5061 − 3.82390i −29.5234 + 24.7731i −13.9192 − 24.1087i −59.8257 − 34.5404i −14.2772 − 80.9699i 33.2149 − 5.85668i
21.18 3.51801 + 0.620321i −2.60001 + 3.09857i −3.04346 − 1.10773i 10.5061 − 3.82390i −11.0690 + 9.28798i 34.0497 + 58.9759i −59.5188 − 34.3632i 11.2244 + 63.6568i 39.3326 − 6.93540i
21.19 3.65190 + 0.643929i −1.10941 + 1.32214i −2.11333 − 0.769187i −10.5061 + 3.82390i −4.90281 + 4.11394i −18.6533 − 32.3084i −58.6052 − 33.8358i 13.5482 + 76.8359i −40.8295 + 7.19935i
21.20 4.04801 + 0.713773i 7.34213 − 8.75001i 0.841792 + 0.306387i −10.5061 + 3.82390i 35.9665 − 30.1795i −41.0247 − 71.0568i −53.7672 − 31.0425i −8.59029 − 48.7179i −45.2581 + 7.98022i
See next 80 embeddings (of 156 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 21.26
Significant digits:
Format:

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 95.5.n.a ✓ 156
19.f odd 18 1 inner 95.5.n.a ✓ 156
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.5.n.a ✓ 156 1.a even 1 1 trivial
95.5.n.a ✓ 156 19.f odd 18 1 inner

Hecke kernels

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