Properties

Label 55.2.a.a
Level 55
Weight 2
Character orbit 55.a
Self dual yes
Analytic conductor 0.439
Analytic rank 0
Dimension 1
CM no
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 55 = 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 55.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.439177211117\)
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

\(f(q)\) \(=\) \( q + q^{2} - q^{4} + q^{5} - 3q^{8} - 3q^{9} + O(q^{10}) \) \( q + q^{2} - q^{4} + q^{5} - 3q^{8} - 3q^{9} + q^{10} - q^{11} + 2q^{13} - q^{16} + 6q^{17} - 3q^{18} - 4q^{19} - q^{20} - q^{22} + 4q^{23} + q^{25} + 2q^{26} + 6q^{29} - 8q^{31} + 5q^{32} + 6q^{34} + 3q^{36} - 2q^{37} - 4q^{38} - 3q^{40} + 2q^{41} + 4q^{43} + q^{44} - 3q^{45} + 4q^{46} - 12q^{47} - 7q^{49} + q^{50} - 2q^{52} - 2q^{53} - q^{55} + 6q^{58} + 4q^{59} - 10q^{61} - 8q^{62} + 7q^{64} + 2q^{65} - 16q^{67} - 6q^{68} + 8q^{71} + 9q^{72} + 14q^{73} - 2q^{74} + 4q^{76} + 8q^{79} - q^{80} + 9q^{81} + 2q^{82} - 4q^{83} + 6q^{85} + 4q^{86} + 3q^{88} + 10q^{89} - 3q^{90} - 4q^{92} - 12q^{94} - 4q^{95} + 10q^{97} - 7q^{98} + 3q^{99} + O(q^{100}) \)

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 0 −1.00000 1.00000 0 0 −3.00000 −3.00000 1.00000
\(n\): 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 55.2.a.a 1
3.b odd 2 1 495.2.a.a 1
4.b odd 2 1 880.2.a.h 1
5.b even 2 1 275.2.a.a 1
5.c odd 4 2 275.2.b.b 2
7.b odd 2 1 2695.2.a.c 1
8.b even 2 1 3520.2.a.p 1
8.d odd 2 1 3520.2.a.n 1
11.b odd 2 1 605.2.a.b 1
11.c even 5 4 605.2.g.a 4
11.d odd 10 4 605.2.g.c 4
12.b even 2 1 7920.2.a.i 1
13.b even 2 1 9295.2.a.b 1
15.d odd 2 1 2475.2.a.i 1
15.e even 4 2 2475.2.c.f 2
20.d odd 2 1 4400.2.a.p 1
20.e even 4 2 4400.2.b.n 2
33.d even 2 1 5445.2.a.i 1
44.c even 2 1 9680.2.a.r 1
55.d odd 2 1 3025.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
55.2.a.a 1 1.a even 1 1 trivial
275.2.a.a 1 5.b even 2 1
275.2.b.b 2 5.c odd 4 2
495.2.a.a 1 3.b odd 2 1
605.2.a.b 1 11.b odd 2 1
605.2.g.a 4 11.c even 5 4
605.2.g.c 4 11.d odd 10 4
880.2.a.h 1 4.b odd 2 1
2475.2.a.i 1 15.d odd 2 1
2475.2.c.f 2 15.e even 4 2
2695.2.a.c 1 7.b odd 2 1
3025.2.a.f 1 55.d odd 2 1
3520.2.a.n 1 8.d odd 2 1
3520.2.a.p 1 8.b even 2 1
4400.2.a.p 1 20.d odd 2 1
4400.2.b.n 2 20.e even 4 2
5445.2.a.i 1 33.d even 2 1
7920.2.a.i 1 12.b even 2 1
9295.2.a.b 1 13.b even 2 1
9680.2.a.r 1 44.c even 2 1

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(11\) \(1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(55))\).