Properties

Label 27.8.a.a
Level 27
Weight 8
Character orbit 27.a
Self dual Yes
Analytic conductor 8.434
Analytic rank 0
Dimension 1
CM disc. -3
Inner twists 2

Related objects

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Newspace parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 27.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(8.43439568807\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $N(\mathrm{U}(1))$

$q$-expansion

\(f(q)\) \(=\) \( q - 128q^{4} + 1763q^{7} + O(q^{10}) \) \( q - 128q^{4} + 1763q^{7} + 12605q^{13} + 16384q^{16} + 14357q^{19} - 78125q^{25} - 225664q^{28} + 178916q^{31} - 615373q^{37} + 1035224q^{43} + 2284626q^{49} - 1613440q^{52} + 1537199q^{61} - 2097152q^{64} - 4058455q^{67} + 1236809q^{73} - 1837696q^{76} - 4245427q^{79} + 22222615q^{91} + 5276357q^{97} + O(q^{100}) \)

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 −128.000 0 0 1763.00 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char. orbit Parity Mult. Self Twist Proved
1.a Even 1 trivial yes
3.b Odd 1 CM by \(\Q(\sqrt{-3}) \) yes

Atkin-Lehner signs

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

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(27))\).