Properties

Label 435.2.a.c
Level $435$
Weight $2$
Character orbit 435.a
Self dual yes
Analytic conductor $3.473$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [435,2,Mod(1,435)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(435, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("435.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 435 = 3 \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 435.a (trivial)

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: yes
Analytic conductor: \(3.47349248793\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q + q^{3} - 2 q^{4} - q^{5} + 2 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{3} - 2 q^{4} - q^{5} + 2 q^{7} + q^{9} + 3 q^{11} - 2 q^{12} + 2 q^{13} - q^{15} + 4 q^{16} + 2 q^{19} + 2 q^{20} + 2 q^{21} + 3 q^{23} + q^{25} + q^{27} - 4 q^{28} - q^{29} + 8 q^{31} + 3 q^{33} - 2 q^{35} - 2 q^{36} - q^{37} + 2 q^{39} - 3 q^{41} - q^{43} - 6 q^{44} - q^{45} - 6 q^{47} + 4 q^{48} - 3 q^{49} - 4 q^{52} - 3 q^{53} - 3 q^{55} + 2 q^{57} - 12 q^{59} + 2 q^{60} + 8 q^{61} + 2 q^{63} - 8 q^{64} - 2 q^{65} + 14 q^{67} + 3 q^{69} - 6 q^{71} - 7 q^{73} + q^{75} - 4 q^{76} + 6 q^{77} - 4 q^{79} - 4 q^{80} + q^{81} + 9 q^{83} - 4 q^{84} - q^{87} - 6 q^{89} + 4 q^{91} - 6 q^{92} + 8 q^{93} - 2 q^{95} + 11 q^{97} + 3 q^{99}+O(q^{100}) \) 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   \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
0 1.00000 −2.00000 −1.00000 0 2.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(5\) \(1\)
\(29\) \(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 435.2.a.c 1
3.b odd 2 1 1305.2.a.d 1
4.b odd 2 1 6960.2.a.b 1
5.b even 2 1 2175.2.a.d 1
5.c odd 4 2 2175.2.c.e 2
15.d odd 2 1 6525.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
435.2.a.c 1 1.a even 1 1 trivial
1305.2.a.d 1 3.b odd 2 1
2175.2.a.d 1 5.b even 2 1
2175.2.c.e 2 5.c odd 4 2
6525.2.a.f 1 15.d odd 2 1
6960.2.a.b 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(435))\):

\( T_{2} \) Copy content Toggle raw display
\( T_{7} - 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T - 1 \) Copy content Toggle raw display
$5$ \( T + 1 \) Copy content Toggle raw display
$7$ \( T - 2 \) Copy content Toggle raw display
$11$ \( T - 3 \) Copy content Toggle raw display
$13$ \( T - 2 \) Copy content Toggle raw display
$17$ \( T \) Copy content Toggle raw display
$19$ \( T - 2 \) Copy content Toggle raw display
$23$ \( T - 3 \) Copy content Toggle raw display
$29$ \( T + 1 \) Copy content Toggle raw display
$31$ \( T - 8 \) Copy content Toggle raw display
$37$ \( T + 1 \) Copy content Toggle raw display
$41$ \( T + 3 \) Copy content Toggle raw display
$43$ \( T + 1 \) Copy content Toggle raw display
$47$ \( T + 6 \) Copy content Toggle raw display
$53$ \( T + 3 \) Copy content Toggle raw display
$59$ \( T + 12 \) Copy content Toggle raw display
$61$ \( T - 8 \) Copy content Toggle raw display
$67$ \( T - 14 \) Copy content Toggle raw display
$71$ \( T + 6 \) Copy content Toggle raw display
$73$ \( T + 7 \) Copy content Toggle raw display
$79$ \( T + 4 \) Copy content Toggle raw display
$83$ \( T - 9 \) Copy content Toggle raw display
$89$ \( T + 6 \) Copy content Toggle raw display
$97$ \( T - 11 \) Copy content Toggle raw display
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