Properties

Label 1425.4.a.d
Level $1425$
Weight $4$
Character orbit 1425.a
Self dual yes
Analytic conductor $84.078$
Analytic rank $1$
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] = [1425,4,Mod(1,1425)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1425, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1425.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1425 = 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1425.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: \(84.0777217582\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 285)
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)
 
\(f(q)\) \(=\) \( q + q^{2} + 3 q^{3} - 7 q^{4} + 3 q^{6} - 4 q^{7} - 15 q^{8} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + 3 q^{3} - 7 q^{4} + 3 q^{6} - 4 q^{7} - 15 q^{8} + 9 q^{9} - 68 q^{11} - 21 q^{12} + 82 q^{13} - 4 q^{14} + 41 q^{16} + 86 q^{17} + 9 q^{18} + 19 q^{19} - 12 q^{21} - 68 q^{22} - 18 q^{23} - 45 q^{24} + 82 q^{26} + 27 q^{27} + 28 q^{28} + 30 q^{29} - 298 q^{31} + 161 q^{32} - 204 q^{33} + 86 q^{34} - 63 q^{36} - 34 q^{37} + 19 q^{38} + 246 q^{39} + 52 q^{41} - 12 q^{42} + 482 q^{43} + 476 q^{44} - 18 q^{46} - 114 q^{47} + 123 q^{48} - 327 q^{49} + 258 q^{51} - 574 q^{52} + 362 q^{53} + 27 q^{54} + 60 q^{56} + 57 q^{57} + 30 q^{58} - 210 q^{59} - 718 q^{61} - 298 q^{62} - 36 q^{63} - 167 q^{64} - 204 q^{66} - 904 q^{67} - 602 q^{68} - 54 q^{69} - 988 q^{71} - 135 q^{72} - 488 q^{73} - 34 q^{74} - 133 q^{76} + 272 q^{77} + 246 q^{78} - 530 q^{79} + 81 q^{81} + 52 q^{82} + 1032 q^{83} + 84 q^{84} + 482 q^{86} + 90 q^{87} + 1020 q^{88} - 880 q^{89} - 328 q^{91} + 126 q^{92} - 894 q^{93} - 114 q^{94} + 483 q^{96} + 246 q^{97} - 327 q^{98} - 612 q^{99}+O(q^{100}) \) 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
1.00000 3.00000 −7.00000 0 3.00000 −4.00000 −15.0000 9.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(5\) \( -1 \)
\(19\) \( -1 \)

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 1425.4.a.d 1
5.b even 2 1 1425.4.a.b 1
5.c odd 4 2 285.4.c.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
285.4.c.a 2 5.c odd 4 2
1425.4.a.b 1 5.b even 2 1
1425.4.a.d 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1425))\):

\( T_{2} - 1 \) Copy content Toggle raw display
\( T_{7} + 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 1 \) Copy content Toggle raw display
$3$ \( T - 3 \) Copy content Toggle raw display
$5$ \( T \) Copy content Toggle raw display
$7$ \( T + 4 \) Copy content Toggle raw display
$11$ \( T + 68 \) Copy content Toggle raw display
$13$ \( T - 82 \) Copy content Toggle raw display
$17$ \( T - 86 \) Copy content Toggle raw display
$19$ \( T - 19 \) Copy content Toggle raw display
$23$ \( T + 18 \) Copy content Toggle raw display
$29$ \( T - 30 \) Copy content Toggle raw display
$31$ \( T + 298 \) Copy content Toggle raw display
$37$ \( T + 34 \) Copy content Toggle raw display
$41$ \( T - 52 \) Copy content Toggle raw display
$43$ \( T - 482 \) Copy content Toggle raw display
$47$ \( T + 114 \) Copy content Toggle raw display
$53$ \( T - 362 \) Copy content Toggle raw display
$59$ \( T + 210 \) Copy content Toggle raw display
$61$ \( T + 718 \) Copy content Toggle raw display
$67$ \( T + 904 \) Copy content Toggle raw display
$71$ \( T + 988 \) Copy content Toggle raw display
$73$ \( T + 488 \) Copy content Toggle raw display
$79$ \( T + 530 \) Copy content Toggle raw display
$83$ \( T - 1032 \) Copy content Toggle raw display
$89$ \( T + 880 \) Copy content Toggle raw display
$97$ \( T - 246 \) Copy content Toggle raw display
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