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Properties

Label 920.2.bv.a
Level $920$
Weight $2$
Character orbit 920.bv
Analytic conductor $7.346$
Analytic rank $0$
Dimension $720$
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] = [920,2,Mod(17,920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(920, base_ring=CyclotomicField(44))
 
chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("920.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.bv (of order \(44\), degree \(20\), 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: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(720\)
Relative dimension: \(36\) over \(\Q(\zeta_{44})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{44}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 720 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
17.1 0 −2.89859 + 1.58275i 0 −2.21695 + 0.291804i 0 0.277250 + 0.370363i 0 4.27482 − 6.65174i 0
17.2 0 −2.83699 + 1.54911i 0 0.823524 − 2.07890i 0 −2.50378 − 3.34466i 0 4.02684 − 6.26588i 0
17.3 0 −2.63218 + 1.43728i 0 2.23215 − 0.132363i 0 −0.0903793 − 0.120733i 0 3.24067 − 5.04257i 0
17.4 0 −2.47093 + 1.34923i 0 −0.998659 + 2.00067i 0 0.191158 + 0.255357i 0 2.66315 − 4.14394i 0
17.5 0 −2.16592 + 1.18268i 0 −1.96360 − 1.06972i 0 0.350713 + 0.468498i 0 1.67054 − 2.59942i 0
17.6 0 −2.01190 + 1.09858i 0 0.842192 + 2.07140i 0 −0.883794 − 1.18061i 0 1.21895 − 1.89673i 0
17.7 0 −1.99325 + 1.08840i 0 2.23196 + 0.135499i 0 2.37528 + 3.17300i 0 1.16653 − 1.81515i 0
17.8 0 −1.72248 + 0.940543i 0 0.500469 − 2.17934i 0 2.14878 + 2.87043i 0 0.460382 − 0.716368i 0
17.9 0 −1.71186 + 0.934747i 0 −1.96254 − 1.07164i 0 −1.50613 − 2.01195i 0 0.434794 − 0.676553i 0
17.10 0 −1.51416 + 0.826793i 0 0.0620735 + 2.23521i 0 2.76190 + 3.68947i 0 −0.0128318 + 0.0199666i 0
17.11 0 −1.25117 + 0.683192i 0 −2.21439 + 0.310585i 0 1.08006 + 1.44279i 0 −0.523240 + 0.814177i 0
17.12 0 −1.21475 + 0.663302i 0 0.933470 − 2.03190i 0 −0.205002 − 0.273851i 0 −0.586283 + 0.912274i 0
17.13 0 −1.07094 + 0.584775i 0 1.80656 + 1.31770i 0 −2.43642 − 3.25467i 0 −0.816980 + 1.27125i 0
17.14 0 −0.908585 + 0.496125i 0 −1.66942 + 1.48763i 0 −2.79645 − 3.73561i 0 −1.04254 + 1.62222i 0
17.15 0 −0.764575 + 0.417490i 0 0.0631286 − 2.23518i 0 −1.48255 − 1.98046i 0 −1.21164 + 1.88536i 0
17.16 0 −0.154469 + 0.0843464i 0 1.48317 − 1.67338i 0 0.708034 + 0.945822i 0 −1.60518 + 2.49770i 0
17.17 0 −0.0822135 + 0.0448920i 0 −1.59045 − 1.57177i 0 3.12275 + 4.17150i 0 −1.61718 + 2.51638i 0
17.18 0 −0.0410298 + 0.0224040i 0 −0.288669 + 2.21736i 0 1.73059 + 2.31180i 0 −1.62074 + 2.52192i 0
17.19 0 −0.00457693 + 0.00249919i 0 2.23374 − 0.101999i 0 −1.95297 − 2.60886i 0 −1.62191 + 2.52374i 0
17.20 0 0.286677 − 0.156537i 0 −2.19869 + 0.407166i 0 −0.456969 − 0.610439i 0 −1.56424 + 2.43401i 0
See next 80 embeddings (of 720 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 17.36
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
23.d odd 22 1 inner
115.l even 44 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 920.2.bv.a ✓ 720
5.c odd 4 1 inner 920.2.bv.a ✓ 720
23.d odd 22 1 inner 920.2.bv.a ✓ 720
115.l even 44 1 inner 920.2.bv.a ✓ 720
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
920.2.bv.a ✓ 720 1.a even 1 1 trivial
920.2.bv.a ✓ 720 5.c odd 4 1 inner
920.2.bv.a ✓ 720 23.d odd 22 1 inner
920.2.bv.a ✓ 720 115.l even 44 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(920, [\chi])\).