Properties

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

Related objects

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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: \(1\)
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

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

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 −3.00000 −2.00000 −3.00000 0 1.00000 6.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

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

Atkin-Lehner signs

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

Hecke kernels

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

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