Properties

Label 121.2.a.b
Level 121
Weight 2
Character orbit 121.a
Self dual Yes
Analytic conductor 0.966
Analytic rank 1
Dimension 1
CM disc. -11
Inner twists 2

Related objects

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Newspace parameters

Level: \( N \) = \( 121 = 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 121.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.966189864457\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q - q^{3} - 2q^{4} - 3q^{5} - 2q^{9} + O(q^{10}) \) \( q - q^{3} - 2q^{4} - 3q^{5} - 2q^{9} + 2q^{12} + 3q^{15} + 4q^{16} + 6q^{20} - 9q^{23} + 4q^{25} + 5q^{27} - 5q^{31} + 4q^{36} + 7q^{37} + 6q^{45} - 12q^{47} - 4q^{48} - 7q^{49} + 6q^{53} - 15q^{59} - 6q^{60} - 8q^{64} + 13q^{67} + 9q^{69} - 3q^{71} - 4q^{75} - 12q^{80} + q^{81} - 9q^{89} + 18q^{92} + 5q^{93} + 17q^{97} + O(q^{100}) \)

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 −1.00000 −2.00000 −3.00000 0 0 0 −2.00000 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
11.b Odd 1 CM by \(\Q(\sqrt{-11}) \) yes

Atkin-Lehner signs

\( p \) Sign
\(11\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(121))\).