Properties

Label 760.2.bv.a
Level $760$
Weight $2$
Character orbit 760.bv
Analytic conductor $6.069$
Analytic rank $0$
Dimension $120$
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] = [760,2,Mod(217,760)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(760, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("760.217");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 760.bv (of order \(12\), degree \(4\), 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: \(6.06863055362\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(30\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 120 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 120 q + 8 q^{11} + 4 q^{23} - 8 q^{25} + 36 q^{33} + 36 q^{41} + 8 q^{43} - 32 q^{45} - 8 q^{47} + 72 q^{51} - 40 q^{55} - 8 q^{57} - 20 q^{63} - 72 q^{67} - 32 q^{73} + 8 q^{77} + 76 q^{81} + 40 q^{83} - 4 q^{85} - 136 q^{87} - 72 q^{91} - 60 q^{93} + 52 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
217.1 0 −3.33013 + 0.892307i 0 −2.14938 + 0.616566i 0 −1.42706 1.42706i 0 7.69551 4.44300i 0
217.2 0 −3.02016 + 0.809249i 0 1.75403 1.38686i 0 −0.311202 0.311202i 0 5.86840 3.38812i 0
217.3 0 −2.83879 + 0.760651i 0 1.80776 + 1.31605i 0 1.74814 + 1.74814i 0 4.88206 2.81866i 0
217.4 0 −2.32691 + 0.623494i 0 −2.16867 + 0.544849i 0 1.17522 + 1.17522i 0 2.42770 1.40163i 0
217.5 0 −2.17220 + 0.582039i 0 −0.102898 + 2.23370i 0 2.97765 + 2.97765i 0 1.78161 1.02861i 0
217.6 0 −2.05819 + 0.551489i 0 0.917131 + 2.03933i 0 −1.67591 1.67591i 0 1.33391 0.770133i 0
217.7 0 −1.84434 + 0.494188i 0 −0.484665 2.18291i 0 −2.21971 2.21971i 0 0.559277 0.322899i 0
217.8 0 −1.62580 + 0.435631i 0 −2.08443 0.809424i 0 −3.36316 3.36316i 0 −0.144631 + 0.0835026i 0
217.9 0 −1.53637 + 0.411668i 0 1.82525 1.29170i 0 1.29575 + 1.29575i 0 −0.407123 + 0.235053i 0
217.10 0 −1.48571 + 0.398094i 0 −1.68119 1.47432i 0 1.98038 + 1.98038i 0 −0.549231 + 0.317098i 0
217.11 0 −1.28291 + 0.343755i 0 0.643100 + 2.14159i 0 −2.68803 2.68803i 0 −1.07038 + 0.617986i 0
217.12 0 −0.683312 + 0.183093i 0 1.03740 1.98086i 0 3.66185 + 3.66185i 0 −2.16468 + 1.24978i 0
217.13 0 −0.653014 + 0.174975i 0 2.17367 0.524542i 0 −1.74329 1.74329i 0 −2.20227 + 1.27148i 0
217.14 0 −0.389775 + 0.104440i 0 2.23580 + 0.0346815i 0 −1.53896 1.53896i 0 −2.45706 + 1.41858i 0
217.15 0 −0.0239568 + 0.00641922i 0 −0.526583 + 2.17318i 0 2.97754 + 2.97754i 0 −2.59754 + 1.49969i 0
217.16 0 0.238684 0.0639551i 0 0.0369332 2.23576i 0 −0.846919 0.846919i 0 −2.54520 + 1.46947i 0
217.17 0 0.304604 0.0816185i 0 −1.67426 + 1.48218i 0 0.297573 + 0.297573i 0 −2.51195 + 1.45028i 0
217.18 0 0.701895 0.188072i 0 −2.06254 0.863675i 0 1.65863 + 1.65863i 0 −2.14079 + 1.23599i 0
217.19 0 0.711431 0.190627i 0 −2.23605 + 0.00824860i 0 0.639892 + 0.639892i 0 −2.12828 + 1.22876i 0
217.20 0 0.882247 0.236397i 0 0.464974 + 2.18719i 0 −1.04303 1.04303i 0 −1.87560 + 1.08288i 0
See next 80 embeddings (of 120 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 217.30
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
19.d odd 6 1 inner
95.l even 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 760.2.bv.a 120
5.c odd 4 1 inner 760.2.bv.a 120
19.d odd 6 1 inner 760.2.bv.a 120
95.l even 12 1 inner 760.2.bv.a 120
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
760.2.bv.a 120 1.a even 1 1 trivial
760.2.bv.a 120 5.c odd 4 1 inner
760.2.bv.a 120 19.d odd 6 1 inner
760.2.bv.a 120 95.l even 12 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(760, [\chi])\).