Properties

Label 3192.2.o.b
Level $3192$
Weight $2$
Character orbit 3192.o
Analytic conductor $25.488$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3192,2,Mod(265,3192)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3192, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3192.265");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3192.o (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: \(25.4882483252\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 40 q^{3} - 2 q^{7} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 40 q + 40 q^{3} - 2 q^{7} + 40 q^{9} - 8 q^{11} + 4 q^{13} - 2 q^{21} - 12 q^{23} - 44 q^{25} + 40 q^{27} - 8 q^{31} - 8 q^{33} - 10 q^{35} + 4 q^{39} + 20 q^{43} + 2 q^{49} - 8 q^{59} - 2 q^{63} - 12 q^{69} - 44 q^{75} - 22 q^{77} + 40 q^{81} + 36 q^{85} + 16 q^{91} - 8 q^{93} + 8 q^{95} - 28 q^{97} - 8 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
265.1 0 1.00000 0 4.42440i 0 −2.30674 1.29575i 0 1.00000 0
265.2 0 1.00000 0 3.81802i 0 −0.437937 2.60925i 0 1.00000 0
265.3 0 1.00000 0 3.49542i 0 −2.01443 + 1.71525i 0 1.00000 0
265.4 0 1.00000 0 3.24542i 0 2.23477 + 1.41627i 0 1.00000 0
265.5 0 1.00000 0 3.23567i 0 2.43709 1.02986i 0 1.00000 0
265.6 0 1.00000 0 3.12999i 0 1.04022 + 2.43268i 0 1.00000 0
265.7 0 1.00000 0 3.06066i 0 2.33587 1.24247i 0 1.00000 0
265.8 0 1.00000 0 2.93144i 0 −2.43014 1.04614i 0 1.00000 0
265.9 0 1.00000 0 2.78430i 0 0.562419 + 2.58528i 0 1.00000 0
265.10 0 1.00000 0 2.21808i 0 0.528301 2.59247i 0 1.00000 0
265.11 0 1.00000 0 1.97676i 0 −2.49077 + 0.892215i 0 1.00000 0
265.12 0 1.00000 0 1.91009i 0 −1.26524 + 2.32361i 0 1.00000 0
265.13 0 1.00000 0 1.43577i 0 −2.08442 1.62948i 0 1.00000 0
265.14 0 1.00000 0 1.33474i 0 −0.149381 2.64153i 0 1.00000 0
265.15 0 1.00000 0 1.08803i 0 2.24871 + 1.39402i 0 1.00000 0
265.16 0 1.00000 0 1.01661i 0 2.64290 + 0.122800i 0 1.00000 0
265.17 0 1.00000 0 0.535557i 0 0.357985 2.62142i 0 1.00000 0
265.18 0 1.00000 0 0.442452i 0 −2.62394 0.339044i 0 1.00000 0
265.19 0 1.00000 0 0.302259i 0 −1.47245 + 2.19816i 0 1.00000 0
265.20 0 1.00000 0 0.0830565i 0 1.88719 + 1.85432i 0 1.00000 0
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 265.40
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
133.c even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 3192.2.o.b yes 40
7.b odd 2 1 3192.2.o.a 40
19.b odd 2 1 3192.2.o.a 40
133.c even 2 1 inner 3192.2.o.b yes 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
3192.2.o.a 40 7.b odd 2 1
3192.2.o.a 40 19.b odd 2 1
3192.2.o.b yes 40 1.a even 1 1 trivial
3192.2.o.b yes 40 133.c even 2 1 inner