Properties

Label 154.4.a.b
Level $154$
Weight $4$
Character orbit 154.a
Self dual yes
Analytic conductor $9.086$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 154.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(9.08629414088\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q - 2 q^{2} + 4 q^{4} + 2 q^{5} - 7 q^{7} - 8 q^{8} - 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{2} + 4 q^{4} + 2 q^{5} - 7 q^{7} - 8 q^{8} - 27 q^{9} - 4 q^{10} + 11 q^{11} + 26 q^{13} + 14 q^{14} + 16 q^{16} - 46 q^{17} + 54 q^{18} - 48 q^{19} + 8 q^{20} - 22 q^{22} - 128 q^{23} - 121 q^{25} - 52 q^{26} - 28 q^{28} - 146 q^{29} - 128 q^{31} - 32 q^{32} + 92 q^{34} - 14 q^{35} - 108 q^{36} - 26 q^{37} + 96 q^{38} - 16 q^{40} + 10 q^{41} + 52 q^{43} + 44 q^{44} - 54 q^{45} + 256 q^{46} - 544 q^{47} + 49 q^{49} + 242 q^{50} + 104 q^{52} + 318 q^{53} + 22 q^{55} + 56 q^{56} + 292 q^{58} - 48 q^{59} + 466 q^{61} + 256 q^{62} + 189 q^{63} + 64 q^{64} + 52 q^{65} + 516 q^{67} - 184 q^{68} + 28 q^{70} - 392 q^{71} + 216 q^{72} + 754 q^{73} + 52 q^{74} - 192 q^{76} - 77 q^{77} + 32 q^{80} + 729 q^{81} - 20 q^{82} + 624 q^{83} - 92 q^{85} - 104 q^{86} - 88 q^{88} - 1590 q^{89} + 108 q^{90} - 182 q^{91} - 512 q^{92} + 1088 q^{94} - 96 q^{95} + 1018 q^{97} - 98 q^{98} - 297 q^{99}+O(q^{100}) \) 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.

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 0 4.00000 2.00000 0 −7.00000 −8.00000 −27.0000 −4.00000
\(n\): 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.b 1
3.b odd 2 1 1386.4.a.j 1
4.b odd 2 1 1232.4.a.e 1
7.b odd 2 1 1078.4.a.b 1
11.b odd 2 1 1694.4.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.4.a.b 1 1.a even 1 1 trivial
1078.4.a.b 1 7.b odd 2 1
1232.4.a.e 1 4.b odd 2 1
1386.4.a.j 1 3.b odd 2 1
1694.4.a.f 1 11.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} \) 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
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 2 \) Copy content Toggle raw display
$7$ \( T + 7 \) Copy content Toggle raw display
$11$ \( T - 11 \) Copy content Toggle raw display
$13$ \( T - 26 \) Copy content Toggle raw display
$17$ \( T + 46 \) Copy content Toggle raw display
$19$ \( T + 48 \) Copy content Toggle raw display
$23$ \( T + 128 \) Copy content Toggle raw display
$29$ \( T + 146 \) Copy content Toggle raw display
$31$ \( T + 128 \) Copy content Toggle raw display
$37$ \( T + 26 \) Copy content Toggle raw display
$41$ \( T - 10 \) Copy content Toggle raw display
$43$ \( T - 52 \) Copy content Toggle raw display
$47$ \( T + 544 \) Copy content Toggle raw display
$53$ \( T - 318 \) Copy content Toggle raw display
$59$ \( T + 48 \) Copy content Toggle raw display
$61$ \( T - 466 \) Copy content Toggle raw display
$67$ \( T - 516 \) Copy content Toggle raw display
$71$ \( T + 392 \) Copy content Toggle raw display
$73$ \( T - 754 \) Copy content Toggle raw display
$79$ \( T \) Copy content Toggle raw display
$83$ \( T - 624 \) Copy content Toggle raw display
$89$ \( T + 1590 \) Copy content Toggle raw display
$97$ \( T - 1018 \) Copy content Toggle raw display
show more
show less