Properties

Label 154.4.a.a
Level $154$
Weight $4$
Character orbit 154.a
Self dual yes
Analytic conductor $9.086$
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] = [154,4,Mod(1,154)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(154, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("154.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 154.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: \(9.08629414088\)
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)
 
\(f(q)\) \(=\) \( q - 2 q^{2} - 5 q^{3} + 4 q^{4} - q^{5} + 10 q^{6} - 7 q^{7} - 8 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{2} - 5 q^{3} + 4 q^{4} - q^{5} + 10 q^{6} - 7 q^{7} - 8 q^{8} - 2 q^{9} + 2 q^{10} - 11 q^{11} - 20 q^{12} - 8 q^{13} + 14 q^{14} + 5 q^{15} + 16 q^{16} + 22 q^{17} + 4 q^{18} + 54 q^{19} - 4 q^{20} + 35 q^{21} + 22 q^{22} + 213 q^{23} + 40 q^{24} - 124 q^{25} + 16 q^{26} + 145 q^{27} - 28 q^{28} + 190 q^{29} - 10 q^{30} + 163 q^{31} - 32 q^{32} + 55 q^{33} - 44 q^{34} + 7 q^{35} - 8 q^{36} + 31 q^{37} - 108 q^{38} + 40 q^{39} + 8 q^{40} + 110 q^{41} - 70 q^{42} + 4 q^{43} - 44 q^{44} + 2 q^{45} - 426 q^{46} - 80 q^{47} - 80 q^{48} + 49 q^{49} + 248 q^{50} - 110 q^{51} - 32 q^{52} - 566 q^{53} - 290 q^{54} + 11 q^{55} + 56 q^{56} - 270 q^{57} - 380 q^{58} + 645 q^{59} + 20 q^{60} + 634 q^{61} - 326 q^{62} + 14 q^{63} + 64 q^{64} + 8 q^{65} - 110 q^{66} - 729 q^{67} + 88 q^{68} - 1065 q^{69} - 14 q^{70} + 431 q^{71} + 16 q^{72} - 918 q^{73} - 62 q^{74} + 620 q^{75} + 216 q^{76} + 77 q^{77} - 80 q^{78} - 254 q^{79} - 16 q^{80} - 671 q^{81} - 220 q^{82} + 904 q^{83} + 140 q^{84} - 22 q^{85} - 8 q^{86} - 950 q^{87} + 88 q^{88} + 901 q^{89} - 4 q^{90} + 56 q^{91} + 852 q^{92} - 815 q^{93} + 160 q^{94} - 54 q^{95} + 160 q^{96} - 89 q^{97} - 98 q^{98} + 22 q^{99}+O(q^{100}) \) 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
−2.00000 −5.00000 4.00000 −1.00000 10.0000 −7.00000 −8.00000 −2.00000 2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(7\) \( +1 \)
\(11\) \( +1 \)

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 154.4.a.a 1
3.b odd 2 1 1386.4.a.k 1
4.b odd 2 1 1232.4.a.g 1
7.b odd 2 1 1078.4.a.c 1
11.b odd 2 1 1694.4.a.e 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.4.a.a 1 1.a even 1 1 trivial
1078.4.a.c 1 7.b odd 2 1
1232.4.a.g 1 4.b odd 2 1
1386.4.a.k 1 3.b odd 2 1
1694.4.a.e 1 11.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 5 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(154))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 2 \) Copy content Toggle raw display
$3$ \( T + 5 \) Copy content Toggle raw display
$5$ \( T + 1 \) Copy content Toggle raw display
$7$ \( T + 7 \) Copy content Toggle raw display
$11$ \( T + 11 \) Copy content Toggle raw display
$13$ \( T + 8 \) Copy content Toggle raw display
$17$ \( T - 22 \) Copy content Toggle raw display
$19$ \( T - 54 \) Copy content Toggle raw display
$23$ \( T - 213 \) Copy content Toggle raw display
$29$ \( T - 190 \) Copy content Toggle raw display
$31$ \( T - 163 \) Copy content Toggle raw display
$37$ \( T - 31 \) Copy content Toggle raw display
$41$ \( T - 110 \) Copy content Toggle raw display
$43$ \( T - 4 \) Copy content Toggle raw display
$47$ \( T + 80 \) Copy content Toggle raw display
$53$ \( T + 566 \) Copy content Toggle raw display
$59$ \( T - 645 \) Copy content Toggle raw display
$61$ \( T - 634 \) Copy content Toggle raw display
$67$ \( T + 729 \) Copy content Toggle raw display
$71$ \( T - 431 \) Copy content Toggle raw display
$73$ \( T + 918 \) Copy content Toggle raw display
$79$ \( T + 254 \) Copy content Toggle raw display
$83$ \( T - 904 \) Copy content Toggle raw display
$89$ \( T - 901 \) Copy content Toggle raw display
$97$ \( T + 89 \) Copy content Toggle raw display
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