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Properties

Label 95.2.p.a
Level $95$
Weight $2$
Character orbit 95.p
Analytic conductor $0.759$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,2,Mod(4,95)]
 
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([9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.p (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: \(0.758578819202\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9} - 15 q^{10} - 12 q^{11} + 6 q^{14} + 3 q^{15} - 42 q^{16} + 12 q^{19} + 42 q^{20} - 54 q^{21} + 24 q^{24} + 12 q^{25} + 12 q^{26} + 18 q^{30} - 42 q^{31} - 36 q^{34} + 6 q^{35} + 18 q^{36} - 48 q^{39} + 66 q^{40} + 6 q^{41} - 6 q^{44} - 9 q^{45} - 6 q^{46} + 12 q^{49} - 18 q^{50} + 108 q^{51} + 24 q^{54} + 36 q^{56} - 36 q^{59} - 114 q^{60} + 48 q^{61} - 18 q^{65} + 180 q^{66} + 66 q^{69} - 123 q^{70} - 24 q^{71} + 84 q^{74} + 72 q^{75} + 66 q^{76} + 48 q^{79} - 39 q^{80} - 78 q^{81} - 54 q^{84} - 84 q^{85} - 42 q^{86} - 12 q^{89} + 18 q^{90} - 30 q^{91} - 72 q^{94} - 63 q^{95} - 240 q^{96} - 36 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
4.1 −0.810919 + 2.22798i 2.25040 − 0.396806i −2.77422 − 2.32785i 2.12266 + 0.703088i −0.940815 + 5.33563i −1.41749 − 0.818386i 3.32944 − 1.92225i 2.08777 − 0.759885i −3.28777 + 4.15909i
4.2 −0.795068 + 2.18443i −1.13113 + 0.199449i −2.60752 − 2.18797i −2.16840 + 0.545927i 0.463643 − 2.62945i −0.124103 − 0.0716510i 2.82626 − 1.63174i −1.57940 + 0.574856i 0.531485 − 5.17077i
4.3 −0.358233 + 0.984236i 0.523379 − 0.0922859i 0.691698 + 0.580404i 0.296741 − 2.21629i −0.0966605 + 0.548189i 2.37320 + 1.37016i −2.63320 + 1.52028i −2.55367 + 0.929459i 2.07505 + 1.08601i
4.4 −0.0854197 + 0.234689i 2.26659 − 0.399662i 1.48431 + 1.24548i −2.12087 + 0.708466i −0.0998158 + 0.566083i −3.42983 − 1.98021i −0.851670 + 0.491712i 2.15864 − 0.785682i 0.0148948 − 0.558261i
4.5 0.0854197 − 0.234689i −2.26659 + 0.399662i 1.48431 + 1.24548i −1.06599 + 1.96562i −0.0998158 + 0.566083i 3.42983 + 1.98021i 0.851670 − 0.491712i 2.15864 − 0.785682i 0.370253 + 0.418078i
4.6 0.358233 − 0.984236i −0.523379 + 0.0922859i 0.691698 + 0.580404i 2.23415 + 0.0926215i −0.0966605 + 0.548189i −2.37320 − 1.37016i 2.63320 − 1.52028i −2.55367 + 0.929459i 0.891507 − 2.16575i
4.7 0.795068 − 2.18443i 1.13113 − 0.199449i −2.60752 − 2.18797i −0.914172 + 2.04066i 0.463643 − 2.62945i 0.124103 + 0.0716510i −2.82626 + 1.63174i −1.57940 + 0.574856i 3.73085 + 3.61941i
4.8 0.810919 − 2.22798i −2.25040 + 0.396806i −2.77422 − 2.32785i −0.323811 − 2.21250i −0.940815 + 5.33563i 1.41749 + 0.818386i −3.32944 + 1.92225i 2.08777 − 0.759885i −5.19199 − 1.07271i
9.1 −1.93197 + 0.340658i −0.120656 − 0.143793i 1.73706 − 0.632239i −1.25335 − 1.85179i 0.282088 + 0.236700i −0.586358 − 0.338534i 0.257316 − 0.148561i 0.514826 − 2.91972i 3.05226 + 3.15062i
9.2 −1.45670 + 0.256855i 1.59617 + 1.90225i 0.176607 − 0.0642796i −0.869056 + 2.06028i −2.81374 − 2.36101i −2.81448 − 1.62494i 2.32124 − 1.34017i −0.549824 + 3.11821i 0.736759 − 3.22442i
9.3 −1.20303 + 0.212126i −0.517072 − 0.616222i −0.477108 + 0.173653i 2.13306 + 0.670867i 0.752768 + 0.631647i 3.28379 + 1.89590i 2.65299 − 1.53170i 0.408578 − 2.31716i −2.70844 − 0.354594i
9.4 −0.240763 + 0.0424530i −1.76019 − 2.09771i −1.82322 + 0.663598i −1.42562 + 1.72267i 0.512843 + 0.430326i −1.68032 − 0.970136i 0.834240 − 0.481648i −0.781184 + 4.43031i 0.270105 − 0.475278i
9.5 0.240763 − 0.0424530i 1.76019 + 2.09771i −1.82322 + 0.663598i 0.0152217 − 2.23602i 0.512843 + 0.430326i 1.68032 + 0.970136i −0.834240 + 0.481648i −0.781184 + 4.43031i −0.0912608 − 0.538996i
9.6 1.20303 − 0.212126i 0.517072 + 0.616222i −0.477108 + 0.173653i 2.06524 + 0.857189i 0.752768 + 0.631647i −3.28379 − 1.89590i −2.65299 + 1.53170i 0.408578 − 2.31716i 2.66638 + 0.593130i
9.7 1.45670 − 0.256855i −1.59617 − 1.90225i 0.176607 − 0.0642796i 0.658585 − 2.13688i −2.81374 − 2.36101i 2.81448 + 1.62494i −2.32124 + 1.34017i −0.549824 + 3.11821i 0.410490 − 3.28195i
9.8 1.93197 − 0.340658i 0.120656 + 0.143793i 1.73706 − 0.632239i −2.15043 + 0.612911i 0.282088 + 0.236700i 0.586358 + 0.338534i −0.257316 + 0.148561i 0.514826 − 2.91972i −3.94576 + 1.91668i
24.1 −0.810919 − 2.22798i 2.25040 + 0.396806i −2.77422 + 2.32785i 2.12266 − 0.703088i −0.940815 − 5.33563i −1.41749 + 0.818386i 3.32944 + 1.92225i 2.08777 + 0.759885i −3.28777 − 4.15909i
24.2 −0.795068 − 2.18443i −1.13113 − 0.199449i −2.60752 + 2.18797i −2.16840 − 0.545927i 0.463643 + 2.62945i −0.124103 + 0.0716510i 2.82626 + 1.63174i −1.57940 − 0.574856i 0.531485 + 5.17077i
24.3 −0.358233 − 0.984236i 0.523379 + 0.0922859i 0.691698 − 0.580404i 0.296741 + 2.21629i −0.0966605 − 0.548189i 2.37320 − 1.37016i −2.63320 − 1.52028i −2.55367 − 0.929459i 2.07505 − 1.08601i
24.4 −0.0854197 − 0.234689i 2.26659 + 0.399662i 1.48431 − 1.24548i −2.12087 − 0.708466i −0.0998158 − 0.566083i −3.42983 + 1.98021i −0.851670 − 0.491712i 2.15864 + 0.785682i 0.0148948 + 0.558261i
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 4.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
19.e even 9 1 inner
95.p even 18 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.2.p.a ✓ 48
3.b odd 2 1 855.2.da.b 48
5.b even 2 1 inner 95.2.p.a ✓ 48
5.c odd 4 2 475.2.l.f 48
15.d odd 2 1 855.2.da.b 48
19.e even 9 1 inner 95.2.p.a ✓ 48
19.e even 9 1 1805.2.b.k 24
19.f odd 18 1 1805.2.b.l 24
57.l odd 18 1 855.2.da.b 48
95.o odd 18 1 1805.2.b.l 24
95.p even 18 1 inner 95.2.p.a ✓ 48
95.p even 18 1 1805.2.b.k 24
95.q odd 36 2 475.2.l.f 48
95.q odd 36 2 9025.2.a.cu 24
95.r even 36 2 9025.2.a.ct 24
285.bd odd 18 1 855.2.da.b 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.2.p.a ✓ 48 1.a even 1 1 trivial
95.2.p.a ✓ 48 5.b even 2 1 inner
95.2.p.a ✓ 48 19.e even 9 1 inner
95.2.p.a ✓ 48 95.p even 18 1 inner
475.2.l.f 48 5.c odd 4 2
475.2.l.f 48 95.q odd 36 2
855.2.da.b 48 3.b odd 2 1
855.2.da.b 48 15.d odd 2 1
855.2.da.b 48 57.l odd 18 1
855.2.da.b 48 285.bd odd 18 1
1805.2.b.k 24 19.e even 9 1
1805.2.b.k 24 95.p even 18 1
1805.2.b.l 24 19.f odd 18 1
1805.2.b.l 24 95.o odd 18 1
9025.2.a.ct 24 95.r even 36 2
9025.2.a.cu 24 95.q odd 36 2

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(95, [\chi])\).