Properties

Label 1900.2.l.d
Level $1900$
Weight $2$
Character orbit 1900.l
Analytic conductor $15.172$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1900,2,Mod(493,1900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1900, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1900.493");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.l (of order \(4\), degree \(2\), 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: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{11} + 24 q^{61} + 24 q^{81}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
493.1 0 −2.05446 + 2.05446i 0 0 0 2.28491 2.28491i 0 5.44162i 0
493.2 0 −2.05446 + 2.05446i 0 0 0 −2.28491 + 2.28491i 0 5.44162i 0
493.3 0 −1.05614 + 1.05614i 0 0 0 −1.45445 + 1.45445i 0 0.769150i 0
493.4 0 −1.05614 + 1.05614i 0 0 0 1.45445 1.45445i 0 0.769150i 0
493.5 0 −0.814717 + 0.814717i 0 0 0 −1.28987 + 1.28987i 0 1.67247i 0
493.6 0 −0.814717 + 0.814717i 0 0 0 1.28987 1.28987i 0 1.67247i 0
493.7 0 0.814717 0.814717i 0 0 0 −1.28987 + 1.28987i 0 1.67247i 0
493.8 0 0.814717 0.814717i 0 0 0 1.28987 1.28987i 0 1.67247i 0
493.9 0 1.05614 1.05614i 0 0 0 −1.45445 + 1.45445i 0 0.769150i 0
493.10 0 1.05614 1.05614i 0 0 0 1.45445 1.45445i 0 0.769150i 0
493.11 0 2.05446 2.05446i 0 0 0 2.28491 2.28491i 0 5.44162i 0
493.12 0 2.05446 2.05446i 0 0 0 −2.28491 + 2.28491i 0 5.44162i 0
1557.1 0 −2.05446 2.05446i 0 0 0 2.28491 + 2.28491i 0 5.44162i 0
1557.2 0 −2.05446 2.05446i 0 0 0 −2.28491 2.28491i 0 5.44162i 0
1557.3 0 −1.05614 1.05614i 0 0 0 −1.45445 1.45445i 0 0.769150i 0
1557.4 0 −1.05614 1.05614i 0 0 0 1.45445 + 1.45445i 0 0.769150i 0
1557.5 0 −0.814717 0.814717i 0 0 0 −1.28987 1.28987i 0 1.67247i 0
1557.6 0 −0.814717 0.814717i 0 0 0 1.28987 + 1.28987i 0 1.67247i 0
1557.7 0 0.814717 + 0.814717i 0 0 0 −1.28987 1.28987i 0 1.67247i 0
1557.8 0 0.814717 + 0.814717i 0 0 0 1.28987 + 1.28987i 0 1.67247i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 493.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
5.c odd 4 2 inner
19.b odd 2 1 inner
95.d odd 2 1 inner
95.g even 4 2 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1900.2.l.d 24
5.b even 2 1 inner 1900.2.l.d 24
5.c odd 4 2 inner 1900.2.l.d 24
19.b odd 2 1 inner 1900.2.l.d 24
95.d odd 2 1 inner 1900.2.l.d 24
95.g even 4 2 inner 1900.2.l.d 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1900.2.l.d 24 1.a even 1 1 trivial
1900.2.l.d 24 5.b even 2 1 inner
1900.2.l.d 24 5.c odd 4 2 inner
1900.2.l.d 24 19.b odd 2 1 inner
1900.2.l.d 24 95.d odd 2 1 inner
1900.2.l.d 24 95.g even 4 2 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{12} + 78T_{3}^{8} + 489T_{3}^{4} + 625 \) acting on \(S_{2}^{\mathrm{new}}(1900, [\chi])\). Copy content Toggle raw display