Properties

Label 27.11.b.a
Level 27
Weight 11
Character orbit 27.b
Self dual Yes
Analytic conductor 17.155
Analytic rank 0
Dimension 1
CM disc. -3
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 11 \)
Character orbit: \([\chi]\) = 27.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(17.1546458222\)
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

\(f(q)\) \(=\) \( q + 1024q^{4} + 10907q^{7} + O(q^{10}) \) \( q + 1024q^{4} + 10907q^{7} - 141961q^{13} + 1048576q^{16} + 4926251q^{19} + 9765625q^{25} + 11168768q^{28} + 49326674q^{31} - 40895593q^{37} - 282780982q^{43} - 163512600q^{49} - 145368064q^{52} - 1354266001q^{61} + 1073741824q^{64} + 2698325411q^{67} + 1957684943q^{73} + 5044481024q^{76} - 6059886949q^{79} - 1548368627q^{91} - 15296411593q^{97} + O(q^{100}) \)

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 1024.00 0 0 10907.0 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 \(S_{11}^{\mathrm{new}}(27, [\chi])\).