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Properties

Label 855.2.p.g
Level $855$
Weight $2$
Character orbit 855.p
Analytic conductor $6.827$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [855,2,Mod(37,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.p (of order \(4\), 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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 40 q^{16} + 16 q^{25} - 8 q^{28} + 56 q^{43} - 16 q^{55} - 56 q^{58} + 48 q^{61} - 64 q^{73} + 32 q^{76} + 8 q^{82} + 72 q^{85}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
37.1 −1.89925 + 1.89925i 0 − 5.21432i −1.30535 + 1.81550i 0 −1.14050 − 1.14050i 6.10480 + 6.10480i 0 −0.968903 − 5.92729i
37.2 −1.89925 + 1.89925i 0 − 5.21432i 1.30535 − 1.81550i 0 −1.14050 − 1.14050i 6.10480 + 6.10480i 0 0.968903 + 5.92729i
37.3 −1.49345 + 1.49345i 0 − 2.46081i −2.22254 + 0.245599i 0 3.02472 + 3.02472i 0.688200 + 0.688200i 0 2.95247 − 3.68605i
37.4 −1.49345 + 1.49345i 0 − 2.46081i 2.22254 − 0.245599i 0 3.02472 + 3.02472i 0.688200 + 0.688200i 0 −2.95247 + 3.68605i
37.5 −1.28935 + 1.28935i 0 − 1.32487i −1.36249 − 1.77303i 0 −1.88423 − 1.88423i −0.870483 − 0.870483i 0 4.04279 + 0.529333i
37.6 −1.28935 + 1.28935i 0 − 1.32487i 1.36249 + 1.77303i 0 −1.88423 − 1.88423i −0.870483 − 0.870483i 0 −4.04279 − 0.529333i
37.7 1.28935 − 1.28935i 0 − 1.32487i −1.36249 − 1.77303i 0 −1.88423 − 1.88423i 0.870483 + 0.870483i 0 −4.04279 − 0.529333i
37.8 1.28935 − 1.28935i 0 − 1.32487i 1.36249 + 1.77303i 0 −1.88423 − 1.88423i 0.870483 + 0.870483i 0 4.04279 + 0.529333i
37.9 1.49345 − 1.49345i 0 − 2.46081i −2.22254 + 0.245599i 0 3.02472 + 3.02472i −0.688200 − 0.688200i 0 −2.95247 + 3.68605i
37.10 1.49345 − 1.49345i 0 − 2.46081i 2.22254 − 0.245599i 0 3.02472 + 3.02472i −0.688200 − 0.688200i 0 2.95247 − 3.68605i
37.11 1.89925 − 1.89925i 0 − 5.21432i −1.30535 + 1.81550i 0 −1.14050 − 1.14050i −6.10480 − 6.10480i 0 0.968903 + 5.92729i
37.12 1.89925 − 1.89925i 0 − 5.21432i 1.30535 − 1.81550i 0 −1.14050 − 1.14050i −6.10480 − 6.10480i 0 −0.968903 − 5.92729i
208.1 −1.89925 − 1.89925i 0 5.21432i −1.30535 − 1.81550i 0 −1.14050 + 1.14050i 6.10480 − 6.10480i 0 −0.968903 + 5.92729i
208.2 −1.89925 − 1.89925i 0 5.21432i 1.30535 + 1.81550i 0 −1.14050 + 1.14050i 6.10480 − 6.10480i 0 0.968903 − 5.92729i
208.3 −1.49345 − 1.49345i 0 2.46081i −2.22254 − 0.245599i 0 3.02472 − 3.02472i 0.688200 − 0.688200i 0 2.95247 + 3.68605i
208.4 −1.49345 − 1.49345i 0 2.46081i 2.22254 + 0.245599i 0 3.02472 − 3.02472i 0.688200 − 0.688200i 0 −2.95247 − 3.68605i
208.5 −1.28935 − 1.28935i 0 1.32487i −1.36249 + 1.77303i 0 −1.88423 + 1.88423i −0.870483 + 0.870483i 0 4.04279 − 0.529333i
208.6 −1.28935 − 1.28935i 0 1.32487i 1.36249 − 1.77303i 0 −1.88423 + 1.88423i −0.870483 + 0.870483i 0 −4.04279 + 0.529333i
208.7 1.28935 + 1.28935i 0 1.32487i −1.36249 + 1.77303i 0 −1.88423 + 1.88423i 0.870483 − 0.870483i 0 −4.04279 + 0.529333i
208.8 1.28935 + 1.28935i 0 1.32487i 1.36249 − 1.77303i 0 −1.88423 + 1.88423i 0.870483 − 0.870483i 0 4.04279 − 0.529333i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 37.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.c odd 4 1 inner
15.e even 4 1 inner
19.b odd 2 1 inner
57.d even 2 1 inner
95.g even 4 1 inner
285.j odd 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 855.2.p.g ✓ 24
3.b odd 2 1 inner 855.2.p.g ✓ 24
5.c odd 4 1 inner 855.2.p.g ✓ 24
15.e even 4 1 inner 855.2.p.g ✓ 24
19.b odd 2 1 inner 855.2.p.g ✓ 24
57.d even 2 1 inner 855.2.p.g ✓ 24
95.g even 4 1 inner 855.2.p.g ✓ 24
285.j odd 4 1 inner 855.2.p.g ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
855.2.p.g ✓ 24 1.a even 1 1 trivial
855.2.p.g ✓ 24 3.b odd 2 1 inner
855.2.p.g ✓ 24 5.c odd 4 1 inner
855.2.p.g ✓ 24 15.e even 4 1 inner
855.2.p.g ✓ 24 19.b odd 2 1 inner
855.2.p.g ✓ 24 57.d even 2 1 inner
855.2.p.g ✓ 24 95.g even 4 1 inner
855.2.p.g ✓ 24 285.j odd 4 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(855, [\chi])\):

\( T_{2}^{12} + 83T_{2}^{8} + 1831T_{2}^{4} + 11449 \) Copy content Toggle raw display
\( T_{7}^{6} + 26T_{7}^{3} + 196T_{7}^{2} + 364T_{7} + 338 \) Copy content Toggle raw display
\( T_{11}^{6} - 30T_{11}^{4} + 242T_{11}^{2} - 250 \) Copy content Toggle raw display