↑

Properties

Label 2088.3.g.a
Level $2088$
Weight $3$
Character orbit 2088.g
Analytic conductor $56.894$
Analytic rank $0$
Dimension $28$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2088,3,Mod(233,2088)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2088, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2088.233");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2088 = 2^{3} \cdot 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2088.g (of order \(2\), degree \(1\), 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: \(56.8938791984\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 32 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q - 32 q^{7} + 40 q^{13} + 24 q^{19} - 140 q^{25} + 56 q^{31} - 200 q^{37} + 144 q^{43} + 268 q^{49} - 184 q^{55} + 40 q^{61} - 288 q^{67} + 88 q^{73} + 136 q^{79} + 16 q^{85} + 544 q^{91} - 24 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
233.1 0 0 0 − 9.62255i 0 −4.43913 0 0 0
233.2 0 0 0 − 9.39291i 0 −11.8742 0 0 0
233.3 0 0 0 − 8.47302i 0 −2.84436 0 0 0
233.4 0 0 0 − 6.40778i 0 4.74069 0 0 0
233.5 0 0 0 − 5.39456i 0 6.98675 0 0 0
233.6 0 0 0 − 5.34424i 0 −4.61061 0 0 0
233.7 0 0 0 − 4.03408i 0 13.9277 0 0 0
233.8 0 0 0 − 3.40576i 0 1.49615 0 0 0
233.9 0 0 0 − 3.27352i 0 −10.7359 0 0 0
233.10 0 0 0 − 2.97269i 0 −1.22259 0 0 0
233.11 0 0 0 − 2.86126i 0 7.67015 0 0 0
233.12 0 0 0 − 2.69783i 0 −1.16890 0 0 0
233.13 0 0 0 − 2.37026i 0 −0.309821 0 0 0
233.14 0 0 0 − 0.396061i 0 −13.6159 0 0 0
233.15 0 0 0 0.396061i 0 −13.6159 0 0 0
233.16 0 0 0 2.37026i 0 −0.309821 0 0 0
233.17 0 0 0 2.69783i 0 −1.16890 0 0 0
233.18 0 0 0 2.86126i 0 7.67015 0 0 0
233.19 0 0 0 2.97269i 0 −1.22259 0 0 0
233.20 0 0 0 3.27352i 0 −10.7359 0 0 0
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 233.28
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2088.3.g.a ✓ 28
3.b odd 2 1 inner 2088.3.g.a ✓ 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2088.3.g.a ✓ 28 1.a even 1 1 trivial
2088.3.g.a ✓ 28 3.b odd 2 1 inner