↑

Properties

Label 968.2.ba.a
Level $968$
Weight $2$
Character orbit 968.ba
Analytic conductor $7.730$
Analytic rank $0$
Dimension $80$
CM discriminant -8
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [968,2,Mod(19,968)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(968, base_ring=CyclotomicField(110))
 
chi = DirichletCharacter(H, H._module([55, 55, 83]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("968.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 968 = 2^{3} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 968.ba (of order \(110\), degree \(40\), 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: \(7.72951891566\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(2\) over \(\Q(\zeta_{110})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{110}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 80 q + 4 q^{3} - 4 q^{4} + 20 q^{6} - 64 q^{9} - 6 q^{11} + 36 q^{12} + 8 q^{16} - 40 q^{18} + 10 q^{19} + 4 q^{22} + 40 q^{24} + 10 q^{25} - 38 q^{27} + 38 q^{33} - 16 q^{34} - 24 q^{36} + 24 q^{38} - 48 q^{44}+ \cdots - 6 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
19.1 −1.01418 + 0.985619i 1.06955 + 3.29173i 0.0571121 − 1.99918i 0 −4.32911 − 2.28423i 0 1.91251 + 2.08382i −7.26452 + 5.27799i 0
19.2 1.01418 − 0.985619i −0.314747 − 0.968691i 0.0571121 − 1.99918i 0 −1.27397 − 0.672204i 0 −1.91251 − 2.08382i 1.58775 − 1.15357i 0
35.1 −0.956256 + 1.04191i 0.599664 − 0.435681i −0.171150 − 1.99266i 0 −0.119492 + 1.04142i 0 2.23984 + 1.72717i −0.757272 + 2.33065i 0
35.2 0.956256 − 1.04191i 2.38115 − 1.73001i −0.171150 − 1.99266i 0 0.474479 − 4.13528i 0 −2.23984 − 1.72717i 1.74991 − 5.38568i 0
51.1 −1.01418 − 0.985619i 1.06955 − 3.29173i 0.0571121 + 1.99918i 0 −4.32911 + 2.28423i 0 1.91251 − 2.08382i −7.26452 − 5.27799i 0
51.2 1.01418 + 0.985619i −0.314747 + 0.968691i 0.0571121 + 1.99918i 0 −1.27397 + 0.672204i 0 −1.91251 + 2.08382i 1.58775 + 1.15357i 0
83.1 −0.956256 − 1.04191i 0.599664 + 0.435681i −0.171150 + 1.99266i 0 −0.119492 − 1.04142i 0 2.23984 − 1.72717i −0.757272 − 2.33065i 0
83.2 0.956256 + 1.04191i 2.38115 + 1.73001i −0.171150 + 1.99266i 0 0.474479 + 4.13528i 0 −2.23984 + 1.72717i 1.74991 + 5.38568i 0
107.1 −0.320315 + 1.37746i 0.484606 + 1.49147i −1.79480 − 0.882442i 0 −2.20966 + 0.189788i 0 1.79043 − 2.18960i 0.437426 − 0.317808i 0
107.2 0.320315 − 1.37746i −1.06144 − 3.26677i −1.79480 − 0.882442i 0 −4.83985 + 0.415695i 0 −1.79043 + 2.18960i −7.11810 + 5.17161i 0
123.1 −1.41364 − 0.0403844i −1.80174 + 1.30904i 1.99674 + 0.114178i 0 2.59986 − 1.77774i 0 −2.81805 − 0.242043i 0.605621 − 1.86391i 0
123.2 1.41364 + 0.0403844i 2.62440 − 1.90674i 1.99674 + 0.114178i 0 3.78696 − 2.58945i 0 2.81805 + 0.242043i 2.32478 − 7.15494i 0
139.1 −0.475246 + 1.33197i −0.567129 + 1.74544i −1.54828 − 1.26602i 0 −2.05535 − 1.58491i 0 2.42212 − 1.46059i −0.297883 − 0.216425i 0
139.2 0.475246 − 1.33197i −0.666923 + 2.05258i −1.54828 − 1.26602i 0 2.41702 + 1.86380i 0 −2.42212 + 1.46059i −1.34124 − 0.974471i 0
171.1 −0.623981 − 1.26911i 2.80217 + 2.03590i −1.22130 + 1.58380i 0 0.835281 − 4.82663i 0 2.77209 + 0.561699i 2.78024 + 8.55669i 0
171.2 0.623981 + 1.26911i −0.975594 − 0.708811i −1.22130 + 1.58380i 0 0.290809 − 1.68042i 0 −2.77209 − 0.561699i −0.477680 − 1.47015i 0
195.1 −0.475246 − 1.33197i −0.567129 − 1.74544i −1.54828 + 1.26602i 0 −2.05535 + 1.58491i 0 2.42212 + 1.46059i −0.297883 + 0.216425i 0
195.2 0.475246 + 1.33197i −0.666923 − 2.05258i −1.54828 + 1.26602i 0 2.41702 − 1.86380i 0 −2.42212 − 1.46059i −1.34124 + 0.974471i 0
211.1 −0.895215 − 1.09480i −1.34665 + 0.978396i −0.397181 + 1.96017i 0 2.27669 + 0.598436i 0 2.50155 − 1.31993i −0.0708524 + 0.218061i 0
211.2 0.895215 + 1.09480i −1.86833 + 1.35742i −0.397181 + 1.96017i 0 −3.15866 − 0.830266i 0 −2.50155 + 1.31993i 0.721009 − 2.21904i 0
See all 80 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 19.2
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.d odd 2 1 CM by \(\Q(\sqrt{-2}) \)
121.h odd 110 1 inner
968.ba even 110 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 968.2.ba.a ✓ 80
8.d odd 2 1 CM 968.2.ba.a ✓ 80
121.h odd 110 1 inner 968.2.ba.a ✓ 80
968.ba even 110 1 inner 968.2.ba.a ✓ 80
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
968.2.ba.a ✓ 80 1.a even 1 1 trivial
968.2.ba.a ✓ 80 8.d odd 2 1 CM
968.2.ba.a ✓ 80 121.h odd 110 1 inner
968.2.ba.a ✓ 80 968.ba even 110 1 inner