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Properties

Label 95.3.j.a
Level $95$
Weight $3$
Character orbit 95.j
Analytic conductor $2.589$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,3,Mod(31,95)]
 
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([0, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.31");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 95.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: \(2.58856251142\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 12 q^{3} + 18 q^{4} - 14 q^{6} - 20 q^{7} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 12 q^{3} + 18 q^{4} - 14 q^{6} - 20 q^{7} + 12 q^{9} + 30 q^{10} - 32 q^{11} - 66 q^{13} - 24 q^{14} - 22 q^{16} + 86 q^{17} - 14 q^{19} + 108 q^{21} - 6 q^{23} + 116 q^{24} - 60 q^{25} + 60 q^{26} - 108 q^{28} - 42 q^{29} - 80 q^{30} - 150 q^{32} - 270 q^{33} - 18 q^{34} - 20 q^{35} + 116 q^{36} + 86 q^{38} - 28 q^{39} + 120 q^{40} - 168 q^{41} + 122 q^{42} - 20 q^{43} - 20 q^{44} + 40 q^{45} + 80 q^{47} + 138 q^{48} + 300 q^{49} + 12 q^{51} - 354 q^{52} - 26 q^{54} + 168 q^{57} - 20 q^{58} - 60 q^{59} - 90 q^{60} - 148 q^{61} + 304 q^{62} - 78 q^{63} - 224 q^{64} - 20 q^{66} - 96 q^{67} + 580 q^{68} - 180 q^{70} + 288 q^{71} + 372 q^{72} - 308 q^{73} - 268 q^{74} + 184 q^{76} + 164 q^{77} - 240 q^{78} + 54 q^{79} - 80 q^{80} - 120 q^{81} + 218 q^{82} + 616 q^{83} + 80 q^{85} + 168 q^{86} - 60 q^{87} - 24 q^{89} - 150 q^{90} + 420 q^{91} - 200 q^{92} - 224 q^{93} + 80 q^{95} - 40 q^{96} + 210 q^{97} - 906 q^{98} + 138 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
31.1 −3.18365 + 1.83808i 2.24660 − 1.29707i 4.75709 − 8.23952i −1.11803 − 1.93649i −4.76826 + 8.25887i −13.5132 20.2710i −1.13519 + 1.96622i 7.11886 + 4.11008i
31.2 −2.40501 + 1.38854i 0.616878 − 0.356155i 1.85606 − 3.21479i −1.11803 − 1.93649i −0.989067 + 1.71311i 11.4122 − 0.799465i −4.24631 + 7.35482i 5.37777 + 3.10486i
31.3 −2.24424 + 1.29571i 4.61922 − 2.66691i 1.35775 − 2.35169i 1.11803 + 1.93649i −6.91110 + 11.9704i 2.84889 − 3.32870i 9.72480 − 16.8439i −5.01828 − 2.89730i
31.4 −1.62941 + 0.940738i −0.453339 + 0.261735i −0.230023 + 0.398411i 1.11803 + 1.93649i 0.492449 − 0.852947i −2.87285 − 8.39147i −4.36299 + 7.55692i −3.64346 − 2.10355i
31.5 −1.25596 + 0.725130i −3.76334 + 2.17276i −0.948373 + 1.64263i −1.11803 − 1.93649i 3.15107 − 5.45782i 0.482708 − 8.55182i 4.94181 − 8.55946i 2.80842 + 1.62144i
31.6 0.258099 − 0.149013i −1.55708 + 0.898979i −1.95559 + 3.38718i −1.11803 − 1.93649i −0.267920 + 0.464051i −4.95425 2.35774i −2.88367 + 4.99467i −0.577127 − 0.333204i
31.7 0.463593 − 0.267656i 0.125201 − 0.0722848i −1.85672 + 3.21593i 1.11803 + 1.93649i 0.0386949 − 0.0670215i 9.24375 4.12909i −4.48955 + 7.77613i 1.03663 + 0.598496i
31.8 0.625777 − 0.361293i 4.26825 − 2.46428i −1.73894 + 3.01192i −1.11803 − 1.93649i 1.78065 − 3.08417i 7.73474 5.40340i 7.64532 − 13.2421i −1.39928 − 0.807875i
31.9 1.51774 − 0.876270i −3.58550 + 2.07009i −0.464301 + 0.804193i 1.11803 + 1.93649i −3.62792 + 6.28374i −13.8338 8.63757i 4.07056 − 7.05042i 3.39378 + 1.95940i
31.10 1.99970 − 1.15453i 3.52499 − 2.03515i 0.665862 − 1.15331i 1.11803 + 1.93649i 4.69928 − 8.13939i −6.47290 6.16119i 3.78371 − 6.55357i 4.47146 + 2.58160i
31.11 2.60665 − 1.50495i 1.18869 − 0.686288i 2.52975 − 4.38165i −1.11803 − 1.93649i 2.06566 − 3.57783i −1.69008 − 3.18897i −3.55802 + 6.16267i −5.82864 − 3.36517i
31.12 3.24671 − 1.87449i −1.23057 + 0.710470i 5.02744 − 8.70778i 1.11803 + 1.93649i −2.66354 + 4.61338i 1.61473 − 22.6996i −3.49047 + 6.04566i 7.25987 + 4.19149i
46.1 −3.18365 − 1.83808i 2.24660 + 1.29707i 4.75709 + 8.23952i −1.11803 + 1.93649i −4.76826 − 8.25887i −13.5132 − 20.2710i −1.13519 − 1.96622i 7.11886 − 4.11008i
46.2 −2.40501 − 1.38854i 0.616878 + 0.356155i 1.85606 + 3.21479i −1.11803 + 1.93649i −0.989067 − 1.71311i 11.4122 0.799465i −4.24631 − 7.35482i 5.37777 − 3.10486i
46.3 −2.24424 − 1.29571i 4.61922 + 2.66691i 1.35775 + 2.35169i 1.11803 − 1.93649i −6.91110 − 11.9704i 2.84889 3.32870i 9.72480 + 16.8439i −5.01828 + 2.89730i
46.4 −1.62941 − 0.940738i −0.453339 − 0.261735i −0.230023 − 0.398411i 1.11803 − 1.93649i 0.492449 + 0.852947i −2.87285 8.39147i −4.36299 − 7.55692i −3.64346 + 2.10355i
46.5 −1.25596 − 0.725130i −3.76334 − 2.17276i −0.948373 − 1.64263i −1.11803 + 1.93649i 3.15107 + 5.45782i 0.482708 8.55182i 4.94181 + 8.55946i 2.80842 − 1.62144i
46.6 0.258099 + 0.149013i −1.55708 − 0.898979i −1.95559 − 3.38718i −1.11803 + 1.93649i −0.267920 − 0.464051i −4.95425 − 2.35774i −2.88367 − 4.99467i −0.577127 + 0.333204i
46.7 0.463593 + 0.267656i 0.125201 + 0.0722848i −1.85672 − 3.21593i 1.11803 − 1.93649i 0.0386949 + 0.0670215i 9.24375 − 4.12909i −4.48955 − 7.77613i 1.03663 − 0.598496i
46.8 0.625777 + 0.361293i 4.26825 + 2.46428i −1.73894 − 3.01192i −1.11803 + 1.93649i 1.78065 + 3.08417i 7.73474 − 5.40340i 7.64532 + 13.2421i −1.39928 + 0.807875i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 31.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
19.d odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.3.j.a ✓ 24
19.d odd 6 1 inner 95.3.j.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.3.j.a ✓ 24 1.a even 1 1 trivial
95.3.j.a ✓ 24 19.d odd 6 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(95, [\chi])\).