Properties

Label 1089.2.a.j
Level 1089
Weight 2
Character orbit 1089.a
Self dual Yes
Analytic conductor 8.696
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1089.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(8.69570878012\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{4} + 2q^{5} - 4q^{7} - 3q^{8} + O(q^{10}) \) \( q + q^{2} - q^{4} + 2q^{5} - 4q^{7} - 3q^{8} + 2q^{10} + 2q^{13} - 4q^{14} - q^{16} - 2q^{17} - 2q^{20} - 8q^{23} - q^{25} + 2q^{26} + 4q^{28} - 6q^{29} - 8q^{31} + 5q^{32} - 2q^{34} - 8q^{35} + 6q^{37} - 6q^{40} - 2q^{41} - 8q^{46} - 8q^{47} + 9q^{49} - q^{50} - 2q^{52} - 6q^{53} + 12q^{56} - 6q^{58} + 4q^{59} - 6q^{61} - 8q^{62} + 7q^{64} + 4q^{65} - 4q^{67} + 2q^{68} - 8q^{70} + 14q^{73} + 6q^{74} + 4q^{79} - 2q^{80} - 2q^{82} + 12q^{83} - 4q^{85} + 6q^{89} - 8q^{91} + 8q^{92} - 8q^{94} + 2q^{97} + 9q^{98} + O(q^{100}) \)

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 2.00000 0 −4.00000 −3.00000 0 2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(11\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1089))\):

\( T_{2} - 1 \)
\( T_{5} - 2 \)
\( T_{7} + 4 \)