Properties

Label 27.9.b.a
Level 27
Weight 9
Character orbit 27.b
Self dual Yes
Analytic conductor 10.999
Analytic rank 0
Dimension 1
CM disc. -3
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 9 \)
Character orbit: \([\chi]\) = 27.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(10.9992224717\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\) \(=\) \(q \) \(\mathstrut +\mathstrut 256q^{4} \) \(\mathstrut +\mathstrut 239q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 256q^{4} \) \(\mathstrut +\mathstrut 239q^{7} \) \(\mathstrut +\mathstrut 56447q^{13} \) \(\mathstrut +\mathstrut 65536q^{16} \) \(\mathstrut +\mathstrut 100559q^{19} \) \(\mathstrut +\mathstrut 390625q^{25} \) \(\mathstrut +\mathstrut 61184q^{28} \) \(\mathstrut -\mathstrut 1809406q^{31} \) \(\mathstrut -\mathstrut 3468481q^{37} \) \(\mathstrut +\mathstrut 3492194q^{43} \) \(\mathstrut -\mathstrut 5707680q^{49} \) \(\mathstrut +\mathstrut 14450432q^{52} \) \(\mathstrut +\mathstrut 24133919q^{61} \) \(\mathstrut +\mathstrut 16777216q^{64} \) \(\mathstrut -\mathstrut 31874833q^{67} \) \(\mathstrut -\mathstrut 55236481q^{73} \) \(\mathstrut +\mathstrut 25743104q^{76} \) \(\mathstrut -\mathstrut 56007121q^{79} \) \(\mathstrut +\mathstrut 13490833q^{91} \) \(\mathstrut -\mathstrut 94775521q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
26.1
0
0 0 256.000 0 0 239.000 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

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2} \) acting on \(S_{9}^{\mathrm{new}}(27, [\chi])\).