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Properties

Label 1840.3.c.b
Level $1840$
Weight $3$
Character orbit 1840.c
Analytic conductor $50.136$
Analytic rank $0$
Dimension $56$
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] = [1840,3,Mod(1151,1840)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1840.1151");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1840.c (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: \(50.1363686423\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 120 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 56 q - 120 q^{9} - 56 q^{13} - 96 q^{17} + 104 q^{21} + 280 q^{25} - 76 q^{29} + 240 q^{33} - 88 q^{37} - 76 q^{41} - 356 q^{49} - 88 q^{53} - 256 q^{57} + 376 q^{61} + 120 q^{65} + 192 q^{73} - 168 q^{77} - 392 q^{81} - 60 q^{85} + 368 q^{89} + 216 q^{93} + 264 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1151.1 0 − 5.32909i 0 −2.23607 0 11.3168i 0 −19.3992 0
1151.2 0 − 5.24733i 0 2.23607 0 − 2.50180i 0 −18.5344 0
1151.3 0 − 5.22053i 0 −2.23607 0 − 0.326739i 0 −18.2539 0
1151.4 0 − 5.16732i 0 2.23607 0 5.17862i 0 −17.7012 0
1151.5 0 − 4.56892i 0 2.23607 0 − 2.46851i 0 −11.8750 0
1151.6 0 − 4.48524i 0 −2.23607 0 − 1.27380i 0 −11.1174 0
1151.7 0 − 4.41875i 0 2.23607 0 4.25333i 0 −10.5254 0
1151.8 0 − 4.39101i 0 −2.23607 0 − 9.33722i 0 −10.2810 0
1151.9 0 − 4.12760i 0 2.23607 0 − 9.93424i 0 −8.03709 0
1151.10 0 − 3.65039i 0 −2.23607 0 − 6.59183i 0 −4.32537 0
1151.11 0 − 3.56153i 0 −2.23607 0 11.6857i 0 −3.68450 0
1151.12 0 − 3.51586i 0 2.23607 0 8.23373i 0 −3.36124 0
1151.13 0 − 3.44787i 0 −2.23607 0 10.1149i 0 −2.88780 0
1151.14 0 − 3.31883i 0 −2.23607 0 − 7.99843i 0 −2.01461 0
1151.15 0 − 3.27428i 0 2.23607 0 − 5.54665i 0 −1.72088 0
1151.16 0 − 2.96566i 0 2.23607 0 5.20785i 0 0.204832 0
1151.17 0 − 2.55509i 0 2.23607 0 8.88631i 0 2.47152 0
1151.18 0 − 2.47004i 0 −2.23607 0 4.00490i 0 2.89892 0
1151.19 0 − 1.90665i 0 −2.23607 0 − 1.76313i 0 5.36467 0
1151.20 0 − 1.78315i 0 2.23607 0 − 11.2760i 0 5.82039 0
See all 56 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1151.56
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1840.3.c.b ✓ 56
4.b odd 2 1 inner 1840.3.c.b ✓ 56
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1840.3.c.b ✓ 56 1.a even 1 1 trivial
1840.3.c.b ✓ 56 4.b odd 2 1 inner