Properties

Label 154.2.a.b
Level $154$
Weight $2$
Character orbit 154.a
Self dual yes
Analytic conductor $1.230$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

Self dual: yes
Analytic conductor: \(1.22969619113\)
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

\(f(q)\) \(=\) \( q - q^{2} + 2 q^{3} + q^{4} + 2 q^{5} - 2 q^{6} - q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + 2 q^{3} + q^{4} + 2 q^{5} - 2 q^{6} - q^{7} - q^{8} + q^{9} - 2 q^{10} + q^{11} + 2 q^{12} - 4 q^{13} + q^{14} + 4 q^{15} + q^{16} - q^{18} + 4 q^{19} + 2 q^{20} - 2 q^{21} - q^{22} + 4 q^{23} - 2 q^{24} - q^{25} + 4 q^{26} - 4 q^{27} - q^{28} + 2 q^{29} - 4 q^{30} - 10 q^{31} - q^{32} + 2 q^{33} - 2 q^{35} + q^{36} - 6 q^{37} - 4 q^{38} - 8 q^{39} - 2 q^{40} + 2 q^{42} - 4 q^{43} + q^{44} + 2 q^{45} - 4 q^{46} + 10 q^{47} + 2 q^{48} + q^{49} + q^{50} - 4 q^{52} - 14 q^{53} + 4 q^{54} + 2 q^{55} + q^{56} + 8 q^{57} - 2 q^{58} + 10 q^{59} + 4 q^{60} - 8 q^{61} + 10 q^{62} - q^{63} + q^{64} - 8 q^{65} - 2 q^{66} + 8 q^{67} + 8 q^{69} + 2 q^{70} - 4 q^{71} - q^{72} + 4 q^{73} + 6 q^{74} - 2 q^{75} + 4 q^{76} - q^{77} + 8 q^{78} + 16 q^{79} + 2 q^{80} - 11 q^{81} + 4 q^{83} - 2 q^{84} + 4 q^{86} + 4 q^{87} - q^{88} + 10 q^{89} - 2 q^{90} + 4 q^{91} + 4 q^{92} - 20 q^{93} - 10 q^{94} + 8 q^{95} - 2 q^{96} + 6 q^{97} - q^{98} + q^{99} + O(q^{100}) \)

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
−1.00000 2.00000 1.00000 2.00000 −2.00000 −1.00000 −1.00000 1.00000 −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 154.2.a.b 1
3.b odd 2 1 1386.2.a.f 1
4.b odd 2 1 1232.2.a.c 1
5.b even 2 1 3850.2.a.o 1
5.c odd 4 2 3850.2.c.d 2
7.b odd 2 1 1078.2.a.b 1
7.c even 3 2 1078.2.e.h 2
7.d odd 6 2 1078.2.e.l 2
8.b even 2 1 4928.2.a.d 1
8.d odd 2 1 4928.2.a.bf 1
11.b odd 2 1 1694.2.a.i 1
21.c even 2 1 9702.2.a.bz 1
28.d even 2 1 8624.2.a.z 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.2.a.b 1 1.a even 1 1 trivial
1078.2.a.b 1 7.b odd 2 1
1078.2.e.h 2 7.c even 3 2
1078.2.e.l 2 7.d odd 6 2
1232.2.a.c 1 4.b odd 2 1
1386.2.a.f 1 3.b odd 2 1
1694.2.a.i 1 11.b odd 2 1
3850.2.a.o 1 5.b even 2 1
3850.2.c.d 2 5.c odd 4 2
4928.2.a.d 1 8.b even 2 1
4928.2.a.bf 1 8.d odd 2 1
8624.2.a.z 1 28.d even 2 1
9702.2.a.bz 1 21.c even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(154))\):

\( T_{3} - 2 \)
\( T_{5} - 2 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( -2 + T \)
$5$ \( -2 + T \)
$7$ \( 1 + T \)
$11$ \( -1 + T \)
$13$ \( 4 + T \)
$17$ \( T \)
$19$ \( -4 + T \)
$23$ \( -4 + T \)
$29$ \( -2 + T \)
$31$ \( 10 + T \)
$37$ \( 6 + T \)
$41$ \( T \)
$43$ \( 4 + T \)
$47$ \( -10 + T \)
$53$ \( 14 + T \)
$59$ \( -10 + T \)
$61$ \( 8 + T \)
$67$ \( -8 + T \)
$71$ \( 4 + T \)
$73$ \( -4 + T \)
$79$ \( -16 + T \)
$83$ \( -4 + T \)
$89$ \( -10 + T \)
$97$ \( -6 + T \)
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