Properties

Label 1148.3.g.a
Level $1148$
Weight $3$
Character orbit 1148.g
Analytic conductor $31.281$
Analytic rank $0$
Dimension $56$
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] = [1148,3,Mod(573,1148)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1148, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1148.573");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1148.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: \(31.2807343486\)
Analytic rank: \(0\)
Dimension: \(56\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q + 136 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 56 q + 136 q^{9} - 12 q^{21} + 40 q^{23} - 324 q^{25} - 164 q^{37} + 100 q^{39} - 20 q^{43} - 80 q^{49} + 220 q^{51} - 420 q^{57} + 324 q^{77} + 224 q^{81} - 308 q^{91}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
573.1 0 −5.69634 0 3.03689i 0 4.13999 + 5.64451i 0 23.4483 0
573.2 0 −5.69634 0 3.03689i 0 4.13999 5.64451i 0 23.4483 0
573.3 0 −4.89631 0 0.632775i 0 −4.64857 + 5.23362i 0 14.9739 0
573.4 0 −4.89631 0 0.632775i 0 −4.64857 5.23362i 0 14.9739 0
573.5 0 −4.85691 0 8.72459i 0 −6.81335 1.60571i 0 14.5896 0
573.6 0 −4.85691 0 8.72459i 0 −6.81335 + 1.60571i 0 14.5896 0
573.7 0 −4.83467 0 5.66595i 0 5.53034 + 4.29131i 0 14.3740 0
573.8 0 −4.83467 0 5.66595i 0 5.53034 4.29131i 0 14.3740 0
573.9 0 −3.63578 0 6.01754i 0 3.80993 5.87235i 0 4.21887 0
573.10 0 −3.63578 0 6.01754i 0 3.80993 + 5.87235i 0 4.21887 0
573.11 0 −3.47135 0 3.69792i 0 −2.49537 + 6.54012i 0 3.05028 0
573.12 0 −3.47135 0 3.69792i 0 −2.49537 6.54012i 0 3.05028 0
573.13 0 −3.09735 0 5.69702i 0 5.23661 + 4.64521i 0 0.593579 0
573.14 0 −3.09735 0 5.69702i 0 5.23661 4.64521i 0 0.593579 0
573.15 0 −2.46507 0 5.99343i 0 −6.99216 0.331276i 0 −2.92345 0
573.16 0 −2.46507 0 5.99343i 0 −6.99216 + 0.331276i 0 −2.92345 0
573.17 0 −2.31144 0 3.75379i 0 6.99996 0.0226023i 0 −3.65724 0
573.18 0 −2.31144 0 3.75379i 0 6.99996 + 0.0226023i 0 −3.65724 0
573.19 0 −2.06233 0 8.76305i 0 −1.14613 + 6.90553i 0 −4.74678 0
573.20 0 −2.06233 0 8.76305i 0 −1.14613 6.90553i 0 −4.74678 0
See all 56 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 573.56
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
41.b even 2 1 inner
287.d odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1148.3.g.a 56
7.b odd 2 1 inner 1148.3.g.a 56
41.b even 2 1 inner 1148.3.g.a 56
287.d odd 2 1 inner 1148.3.g.a 56
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1148.3.g.a 56 1.a even 1 1 trivial
1148.3.g.a 56 7.b odd 2 1 inner
1148.3.g.a 56 41.b even 2 1 inner
1148.3.g.a 56 287.d odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1148, [\chi])\).