Properties

Label 179.2.a.a
Level 179
Weight 2
Character orbit 179.a
Self dual yes
Analytic conductor 1.429
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 179 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 179.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.42932219618\)
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

\(f(q)\) \(=\) \( q + 2q^{2} + 2q^{4} + 3q^{5} - 4q^{7} - 3q^{9} + O(q^{10}) \) \( q + 2q^{2} + 2q^{4} + 3q^{5} - 4q^{7} - 3q^{9} + 6q^{10} + 4q^{11} - q^{13} - 8q^{14} - 4q^{16} + q^{17} - 6q^{18} - 3q^{19} + 6q^{20} + 8q^{22} + 6q^{23} + 4q^{25} - 2q^{26} - 8q^{28} + 3q^{29} - 8q^{31} - 8q^{32} + 2q^{34} - 12q^{35} - 6q^{36} + 2q^{37} - 6q^{38} + 12q^{41} - 11q^{43} + 8q^{44} - 9q^{45} + 12q^{46} + q^{47} + 9q^{49} + 8q^{50} - 2q^{52} + 12q^{55} + 6q^{58} - 5q^{59} + 14q^{61} - 16q^{62} + 12q^{63} - 8q^{64} - 3q^{65} - 9q^{67} + 2q^{68} - 24q^{70} + 10q^{73} + 4q^{74} - 6q^{76} - 16q^{77} + 10q^{79} - 12q^{80} + 9q^{81} + 24q^{82} + 17q^{83} + 3q^{85} - 22q^{86} - q^{89} - 18q^{90} + 4q^{91} + 12q^{92} + 2q^{94} - 9q^{95} - 14q^{97} + 18q^{98} - 12q^{99} + O(q^{100}) \)

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 0 2.00000 3.00000 0 −4.00000 0 −3.00000 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 179.2.a.a 1
3.b odd 2 1 1611.2.a.a 1
4.b odd 2 1 2864.2.a.b 1
5.b even 2 1 4475.2.a.a 1
7.b odd 2 1 8771.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
179.2.a.a 1 1.a even 1 1 trivial
1611.2.a.a 1 3.b odd 2 1
2864.2.a.b 1 4.b odd 2 1
4475.2.a.a 1 5.b even 2 1
8771.2.a.b 1 7.b odd 2 1

Atkin-Lehner signs

\( p \) Sign
\(179\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(179))\).