Properties

Label 54.2.a.a
Level $54$
Weight $2$
Character orbit 54.a
Self dual yes
Analytic conductor $0.431$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 54.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.431192170915\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} + 3q^{5} - q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} + 3q^{5} - q^{7} - q^{8} - 3q^{10} - 3q^{11} - 4q^{13} + q^{14} + q^{16} + 2q^{19} + 3q^{20} + 3q^{22} - 6q^{23} + 4q^{25} + 4q^{26} - q^{28} + 6q^{29} + 5q^{31} - q^{32} - 3q^{35} + 2q^{37} - 2q^{38} - 3q^{40} - 6q^{41} - 10q^{43} - 3q^{44} + 6q^{46} + 6q^{47} - 6q^{49} - 4q^{50} - 4q^{52} + 9q^{53} - 9q^{55} + q^{56} - 6q^{58} + 12q^{59} + 8q^{61} - 5q^{62} + q^{64} - 12q^{65} + 14q^{67} + 3q^{70} - 7q^{73} - 2q^{74} + 2q^{76} + 3q^{77} + 8q^{79} + 3q^{80} + 6q^{82} - 3q^{83} + 10q^{86} + 3q^{88} - 18q^{89} + 4q^{91} - 6q^{92} - 6q^{94} + 6q^{95} - q^{97} + 6q^{98} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)

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 54.2.a.a 1
3.b odd 2 1 54.2.a.b yes 1
4.b odd 2 1 432.2.a.g 1
5.b even 2 1 1350.2.a.r 1
5.c odd 4 2 1350.2.c.b 2
7.b odd 2 1 2646.2.a.a 1
8.b even 2 1 1728.2.a.c 1
8.d odd 2 1 1728.2.a.d 1
9.c even 3 2 162.2.c.c 2
9.d odd 6 2 162.2.c.b 2
11.b odd 2 1 6534.2.a.bc 1
12.b even 2 1 432.2.a.b 1
13.b even 2 1 9126.2.a.u 1
15.d odd 2 1 1350.2.a.h 1
15.e even 4 2 1350.2.c.k 2
21.c even 2 1 2646.2.a.bd 1
24.f even 2 1 1728.2.a.z 1
24.h odd 2 1 1728.2.a.y 1
33.d even 2 1 6534.2.a.b 1
36.f odd 6 2 1296.2.i.c 2
36.h even 6 2 1296.2.i.o 2
39.d odd 2 1 9126.2.a.r 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
54.2.a.a 1 1.a even 1 1 trivial
54.2.a.b yes 1 3.b odd 2 1
162.2.c.b 2 9.d odd 6 2
162.2.c.c 2 9.c even 3 2
432.2.a.b 1 12.b even 2 1
432.2.a.g 1 4.b odd 2 1
1296.2.i.c 2 36.f odd 6 2
1296.2.i.o 2 36.h even 6 2
1350.2.a.h 1 15.d odd 2 1
1350.2.a.r 1 5.b even 2 1
1350.2.c.b 2 5.c odd 4 2
1350.2.c.k 2 15.e even 4 2
1728.2.a.c 1 8.b even 2 1
1728.2.a.d 1 8.d odd 2 1
1728.2.a.y 1 24.h odd 2 1
1728.2.a.z 1 24.f even 2 1
2646.2.a.a 1 7.b odd 2 1
2646.2.a.bd 1 21.c even 2 1
6534.2.a.b 1 33.d even 2 1
6534.2.a.bc 1 11.b odd 2 1
9126.2.a.r 1 39.d odd 2 1
9126.2.a.u 1 13.b even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} - 3 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(54))\).