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Properties

Label 1848.2.q.a
Level $1848$
Weight $2$
Character orbit 1848.q
Analytic conductor $14.756$
Analytic rank $0$
Dimension $24$
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] = [1848,2,Mod(769,1848)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1848, 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("1848.769");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1848.q (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: \(14.7563542935\)
Analytic rank: \(0\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{7} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{7} - 24 q^{9} + 4 q^{11} - 4 q^{15} + 4 q^{17} + 4 q^{19} - 24 q^{23} - 8 q^{25} + 8 q^{33} + 16 q^{35} + 8 q^{37} - 20 q^{41} + 4 q^{49} - 24 q^{53} - 8 q^{55} + 8 q^{61} + 4 q^{63} - 8 q^{67} + 4 q^{73} - 8 q^{77} + 24 q^{81} - 4 q^{83} - 8 q^{87} - 4 q^{91} + 12 q^{93} - 4 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
769.1 0 − 1.00000i 0 − 3.77374i 0 2.27938 + 1.34328i 0 −1.00000 0
769.2 0 − 1.00000i 0 − 3.27939i 0 −2.61990 − 0.368974i 0 −1.00000 0
769.3 0 − 1.00000i 0 − 2.50231i 0 −2.45571 + 0.984620i 0 −1.00000 0
769.4 0 − 1.00000i 0 − 2.32410i 0 0.212212 − 2.63723i 0 −1.00000 0
769.5 0 − 1.00000i 0 − 0.883273i 0 0.763345 + 2.53324i 0 −1.00000 0
769.6 0 − 1.00000i 0 − 0.210416i 0 2.16457 − 1.52140i 0 −1.00000 0
769.7 0 − 1.00000i 0 0.331450i 0 1.23509 + 2.33977i 0 −1.00000 0
769.8 0 − 1.00000i 0 1.09147i 0 2.61768 − 0.384362i 0 −1.00000 0
769.9 0 − 1.00000i 0 1.64449i 0 −2.63155 + 0.273742i 0 −1.00000 0
769.10 0 − 1.00000i 0 1.71581i 0 −1.06269 − 2.42295i 0 −1.00000 0
769.11 0 − 1.00000i 0 2.64261i 0 −1.38114 + 2.25664i 0 −1.00000 0
769.12 0 − 1.00000i 0 3.54741i 0 −1.12129 − 2.39640i 0 −1.00000 0
769.13 0 1.00000i 0 − 3.54741i 0 −1.12129 + 2.39640i 0 −1.00000 0
769.14 0 1.00000i 0 − 2.64261i 0 −1.38114 − 2.25664i 0 −1.00000 0
769.15 0 1.00000i 0 − 1.71581i 0 −1.06269 + 2.42295i 0 −1.00000 0
769.16 0 1.00000i 0 − 1.64449i 0 −2.63155 − 0.273742i 0 −1.00000 0
769.17 0 1.00000i 0 − 1.09147i 0 2.61768 + 0.384362i 0 −1.00000 0
769.18 0 1.00000i 0 − 0.331450i 0 1.23509 − 2.33977i 0 −1.00000 0
769.19 0 1.00000i 0 0.210416i 0 2.16457 + 1.52140i 0 −1.00000 0
769.20 0 1.00000i 0 0.883273i 0 0.763345 − 2.53324i 0 −1.00000 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 769.24
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1848.2.q.a ✓ 24
4.b odd 2 1 3696.2.q.g 24
7.b odd 2 1 1848.2.q.b yes 24
11.b odd 2 1 1848.2.q.b yes 24
28.d even 2 1 3696.2.q.f 24
44.c even 2 1 3696.2.q.f 24
77.b even 2 1 inner 1848.2.q.a ✓ 24
308.g odd 2 1 3696.2.q.g 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1848.2.q.a ✓ 24 1.a even 1 1 trivial
1848.2.q.a ✓ 24 77.b even 2 1 inner
1848.2.q.b yes 24 7.b odd 2 1
1848.2.q.b yes 24 11.b odd 2 1
3696.2.q.f 24 28.d even 2 1
3696.2.q.f 24 44.c even 2 1
3696.2.q.g 24 4.b odd 2 1
3696.2.q.g 24 308.g odd 2 1