Properties

Label 27.2.a.a
Level 27
Weight 2
Character orbit 27.a
Self dual yes
Analytic conductor 0.216
Analytic rank 0
Dimension 1
CM discriminant -3
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 27.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.215596085457\)
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: $N(\mathrm{U}(1))$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{4} - q^{7} + O(q^{10}) \) \( q - 2q^{4} - q^{7} + 5q^{13} + 4q^{16} - 7q^{19} - 5q^{25} + 2q^{28} - 4q^{31} + 11q^{37} + 8q^{43} - 6q^{49} - 10q^{52} - q^{61} - 8q^{64} + 5q^{67} - 7q^{73} + 14q^{76} + 17q^{79} - 5q^{91} - 19q^{97} + O(q^{100}) \)

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

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 CM by \(\Q(\sqrt{-3}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 27.2.a.a 1
3.b odd 2 1 CM 27.2.a.a 1
4.b odd 2 1 432.2.a.e 1
5.b even 2 1 675.2.a.e 1
5.c odd 4 2 675.2.b.f 2
7.b odd 2 1 1323.2.a.i 1
8.b even 2 1 1728.2.a.n 1
8.d odd 2 1 1728.2.a.o 1
9.c even 3 2 81.2.c.a 2
9.d odd 6 2 81.2.c.a 2
11.b odd 2 1 3267.2.a.f 1
12.b even 2 1 432.2.a.e 1
13.b even 2 1 4563.2.a.e 1
15.d odd 2 1 675.2.a.e 1
15.e even 4 2 675.2.b.f 2
17.b even 2 1 7803.2.a.k 1
19.b odd 2 1 9747.2.a.f 1
21.c even 2 1 1323.2.a.i 1
24.f even 2 1 1728.2.a.o 1
24.h odd 2 1 1728.2.a.n 1
27.e even 9 6 729.2.e.f 6
27.f odd 18 6 729.2.e.f 6
33.d even 2 1 3267.2.a.f 1
36.f odd 6 2 1296.2.i.i 2
36.h even 6 2 1296.2.i.i 2
39.d odd 2 1 4563.2.a.e 1
51.c odd 2 1 7803.2.a.k 1
57.d even 2 1 9747.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
27.2.a.a 1 1.a even 1 1 trivial
27.2.a.a 1 3.b odd 2 1 CM
81.2.c.a 2 9.c even 3 2
81.2.c.a 2 9.d odd 6 2
432.2.a.e 1 4.b odd 2 1
432.2.a.e 1 12.b even 2 1
675.2.a.e 1 5.b even 2 1
675.2.a.e 1 15.d odd 2 1
675.2.b.f 2 5.c odd 4 2
675.2.b.f 2 15.e even 4 2
729.2.e.f 6 27.e even 9 6
729.2.e.f 6 27.f odd 18 6
1296.2.i.i 2 36.f odd 6 2
1296.2.i.i 2 36.h even 6 2
1323.2.a.i 1 7.b odd 2 1
1323.2.a.i 1 21.c even 2 1
1728.2.a.n 1 8.b even 2 1
1728.2.a.n 1 24.h odd 2 1
1728.2.a.o 1 8.d odd 2 1
1728.2.a.o 1 24.f even 2 1
3267.2.a.f 1 11.b odd 2 1
3267.2.a.f 1 33.d even 2 1
4563.2.a.e 1 13.b even 2 1
4563.2.a.e 1 39.d odd 2 1
7803.2.a.k 1 17.b even 2 1
7803.2.a.k 1 51.c odd 2 1
9747.2.a.f 1 19.b odd 2 1
9747.2.a.f 1 57.d even 2 1

Atkin-Lehner signs

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

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\).