Properties

Label 154.4.a.c
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)
 
\(f(q)\) \(=\) \( q + 2 q^{2} - 10 q^{3} + 4 q^{4} - 14 q^{5} - 20 q^{6} + 7 q^{7} + 8 q^{8} + 73 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{2} - 10 q^{3} + 4 q^{4} - 14 q^{5} - 20 q^{6} + 7 q^{7} + 8 q^{8} + 73 q^{9} - 28 q^{10} - 11 q^{11} - 40 q^{12} - 16 q^{13} + 14 q^{14} + 140 q^{15} + 16 q^{16} + 108 q^{17} + 146 q^{18} + 116 q^{19} - 56 q^{20} - 70 q^{21} - 22 q^{22} + 68 q^{23} - 80 q^{24} + 71 q^{25} - 32 q^{26} - 460 q^{27} + 28 q^{28} + 122 q^{29} + 280 q^{30} - 262 q^{31} + 32 q^{32} + 110 q^{33} + 216 q^{34} - 98 q^{35} + 292 q^{36} + 130 q^{37} + 232 q^{38} + 160 q^{39} - 112 q^{40} + 204 q^{41} - 140 q^{42} - 396 q^{43} - 44 q^{44} - 1022 q^{45} + 136 q^{46} + 166 q^{47} - 160 q^{48} + 49 q^{49} + 142 q^{50} - 1080 q^{51} - 64 q^{52} + 442 q^{53} - 920 q^{54} + 154 q^{55} + 56 q^{56} - 1160 q^{57} + 244 q^{58} + 702 q^{59} + 560 q^{60} + 196 q^{61} - 524 q^{62} + 511 q^{63} + 64 q^{64} + 224 q^{65} + 220 q^{66} - 416 q^{67} + 432 q^{68} - 680 q^{69} - 196 q^{70} + 492 q^{71} + 584 q^{72} + 408 q^{73} + 260 q^{74} - 710 q^{75} + 464 q^{76} - 77 q^{77} + 320 q^{78} + 600 q^{79} - 224 q^{80} + 2629 q^{81} + 408 q^{82} - 1212 q^{83} - 280 q^{84} - 1512 q^{85} - 792 q^{86} - 1220 q^{87} - 88 q^{88} + 1146 q^{89} - 2044 q^{90} - 112 q^{91} + 272 q^{92} + 2620 q^{93} + 332 q^{94} - 1624 q^{95} - 320 q^{96} - 482 q^{97} + 98 q^{98} - 803 q^{99}+O(q^{100}) \) 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 −10.0000 4.00000 −14.0000 −20.0000 7.00000 8.00000 73.0000 −28.0000
\(n\): 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.c 1
3.b odd 2 1 1386.4.a.g 1
4.b odd 2 1 1232.4.a.i 1
7.b odd 2 1 1078.4.a.h 1
11.b odd 2 1 1694.4.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.4.a.c 1 1.a even 1 1 trivial
1078.4.a.h 1 7.b odd 2 1
1232.4.a.i 1 4.b odd 2 1
1386.4.a.g 1 3.b odd 2 1
1694.4.a.a 1 11.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 10 \) 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
$3$ \( T + 10 \) Copy content Toggle raw display
$5$ \( T + 14 \) Copy content Toggle raw display
$7$ \( T - 7 \) Copy content Toggle raw display
$11$ \( T + 11 \) Copy content Toggle raw display
$13$ \( T + 16 \) Copy content Toggle raw display
$17$ \( T - 108 \) Copy content Toggle raw display
$19$ \( T - 116 \) Copy content Toggle raw display
$23$ \( T - 68 \) Copy content Toggle raw display
$29$ \( T - 122 \) Copy content Toggle raw display
$31$ \( T + 262 \) Copy content Toggle raw display
$37$ \( T - 130 \) Copy content Toggle raw display
$41$ \( T - 204 \) Copy content Toggle raw display
$43$ \( T + 396 \) Copy content Toggle raw display
$47$ \( T - 166 \) Copy content Toggle raw display
$53$ \( T - 442 \) Copy content Toggle raw display
$59$ \( T - 702 \) Copy content Toggle raw display
$61$ \( T - 196 \) Copy content Toggle raw display
$67$ \( T + 416 \) Copy content Toggle raw display
$71$ \( T - 492 \) Copy content Toggle raw display
$73$ \( T - 408 \) Copy content Toggle raw display
$79$ \( T - 600 \) Copy content Toggle raw display
$83$ \( T + 1212 \) Copy content Toggle raw display
$89$ \( T - 1146 \) Copy content Toggle raw display
$97$ \( T + 482 \) Copy content Toggle raw display
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