Properties

Label 141.2.a.e
Level $141$
Weight $2$
Character orbit 141.a
Self dual yes
Analytic conductor $1.126$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 141 = 3 \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 141.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.12589066850\)
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

\(f(q)\) \(=\) \( q + 2q^{2} + q^{3} + 2q^{4} - q^{5} + 2q^{6} - 3q^{7} + q^{9} + O(q^{10}) \) \( q + 2q^{2} + q^{3} + 2q^{4} - q^{5} + 2q^{6} - 3q^{7} + q^{9} - 2q^{10} + q^{11} + 2q^{12} - 2q^{13} - 6q^{14} - q^{15} - 4q^{16} + 2q^{17} + 2q^{18} + 6q^{19} - 2q^{20} - 3q^{21} + 2q^{22} + 3q^{23} - 4q^{25} - 4q^{26} + q^{27} - 6q^{28} + 3q^{29} - 2q^{30} + 2q^{31} - 8q^{32} + q^{33} + 4q^{34} + 3q^{35} + 2q^{36} - 7q^{37} + 12q^{38} - 2q^{39} + 10q^{41} - 6q^{42} - 10q^{43} + 2q^{44} - q^{45} + 6q^{46} - q^{47} - 4q^{48} + 2q^{49} - 8q^{50} + 2q^{51} - 4q^{52} + 4q^{53} + 2q^{54} - q^{55} + 6q^{57} + 6q^{58} + 8q^{59} - 2q^{60} - 10q^{61} + 4q^{62} - 3q^{63} - 8q^{64} + 2q^{65} + 2q^{66} + 10q^{67} + 4q^{68} + 3q^{69} + 6q^{70} - 14q^{71} - 10q^{73} - 14q^{74} - 4q^{75} + 12q^{76} - 3q^{77} - 4q^{78} + 17q^{79} + 4q^{80} + q^{81} + 20q^{82} + 8q^{83} - 6q^{84} - 2q^{85} - 20q^{86} + 3q^{87} + 6q^{89} - 2q^{90} + 6q^{91} + 6q^{92} + 2q^{93} - 2q^{94} - 6q^{95} - 8q^{96} + q^{97} + 4q^{98} + q^{99} + O(q^{100}) \)

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
2.00000 1.00000 2.00000 −1.00000 2.00000 −3.00000 0 1.00000 −2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(47\) \(1\)

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 141.2.a.e 1
3.b odd 2 1 423.2.a.b 1
4.b odd 2 1 2256.2.a.e 1
5.b even 2 1 3525.2.a.c 1
7.b odd 2 1 6909.2.a.k 1
8.b even 2 1 9024.2.a.n 1
8.d odd 2 1 9024.2.a.bq 1
12.b even 2 1 6768.2.a.n 1
47.b odd 2 1 6627.2.a.i 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
141.2.a.e 1 1.a even 1 1 trivial
423.2.a.b 1 3.b odd 2 1
2256.2.a.e 1 4.b odd 2 1
3525.2.a.c 1 5.b even 2 1
6627.2.a.i 1 47.b odd 2 1
6768.2.a.n 1 12.b even 2 1
6909.2.a.k 1 7.b odd 2 1
9024.2.a.n 1 8.b even 2 1
9024.2.a.bq 1 8.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(141))\):

\( T_{2} - 2 \)
\( T_{5} + 1 \)

Hecke characteristic polynomials

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