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Properties

Label 1932.3.d.a
Level $1932$
Weight $3$
Character orbit 1932.d
Analytic conductor $52.643$
Analytic rank $0$
Dimension $48$
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] = [1932,3,Mod(505,1932)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1932, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1932.505");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1932.d (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: \(52.6431870744\)
Analytic rank: \(0\)
Dimension: \(48\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 144 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q + 144 q^{9} + 16 q^{13} + 60 q^{23} - 240 q^{25} - 96 q^{29} - 8 q^{31} - 56 q^{35} - 96 q^{39} - 152 q^{41} + 168 q^{47} - 336 q^{49} + 296 q^{55} - 248 q^{59} + 48 q^{69} + 112 q^{71} + 416 q^{73} - 48 q^{75} + 432 q^{81} + 88 q^{85} - 264 q^{87} - 272 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
505.1 0 −1.73205 0 − 9.42025i 0 − 2.64575i 0 3.00000 0
505.2 0 −1.73205 0 − 7.97139i 0 2.64575i 0 3.00000 0
505.3 0 −1.73205 0 − 7.27445i 0 − 2.64575i 0 3.00000 0
505.4 0 −1.73205 0 − 6.21125i 0 2.64575i 0 3.00000 0
505.5 0 −1.73205 0 − 6.05249i 0 2.64575i 0 3.00000 0
505.6 0 −1.73205 0 − 5.84116i 0 − 2.64575i 0 3.00000 0
505.7 0 −1.73205 0 − 5.27153i 0 − 2.64575i 0 3.00000 0
505.8 0 −1.73205 0 − 2.17358i 0 − 2.64575i 0 3.00000 0
505.9 0 −1.73205 0 − 1.64375i 0 2.64575i 0 3.00000 0
505.10 0 −1.73205 0 − 1.61322i 0 2.64575i 0 3.00000 0
505.11 0 −1.73205 0 − 0.642371i 0 2.64575i 0 3.00000 0
505.12 0 −1.73205 0 − 0.554993i 0 2.64575i 0 3.00000 0
505.13 0 −1.73205 0 0.554993i 0 − 2.64575i 0 3.00000 0
505.14 0 −1.73205 0 0.642371i 0 − 2.64575i 0 3.00000 0
505.15 0 −1.73205 0 1.61322i 0 − 2.64575i 0 3.00000 0
505.16 0 −1.73205 0 1.64375i 0 − 2.64575i 0 3.00000 0
505.17 0 −1.73205 0 2.17358i 0 2.64575i 0 3.00000 0
505.18 0 −1.73205 0 5.27153i 0 2.64575i 0 3.00000 0
505.19 0 −1.73205 0 5.84116i 0 2.64575i 0 3.00000 0
505.20 0 −1.73205 0 6.05249i 0 − 2.64575i 0 3.00000 0
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 505.48
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1932.3.d.a ✓ 48
23.b odd 2 1 inner 1932.3.d.a ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1932.3.d.a ✓ 48 1.a even 1 1 trivial
1932.3.d.a ✓ 48 23.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1932, [\chi])\).