Properties

Label 123.2.a.b
Level 123
Weight 2
Character orbit 123.a
Self dual Yes
Analytic conductor 0.982
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 123 = 3 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 123.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.982159944862\)
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

\(f(q)\) \(=\) \( q - q^{3} - 2q^{4} - 2q^{5} - 4q^{7} + q^{9} + O(q^{10}) \) \( q - q^{3} - 2q^{4} - 2q^{5} - 4q^{7} + q^{9} + 5q^{11} + 2q^{12} - 4q^{13} + 2q^{15} + 4q^{16} - 5q^{17} - 2q^{19} + 4q^{20} + 4q^{21} + 4q^{23} - q^{25} - q^{27} + 8q^{28} + q^{29} - 5q^{31} - 5q^{33} + 8q^{35} - 2q^{36} - 7q^{37} + 4q^{39} - q^{41} + 7q^{43} - 10q^{44} - 2q^{45} + 7q^{47} - 4q^{48} + 9q^{49} + 5q^{51} + 8q^{52} - 14q^{53} - 10q^{55} + 2q^{57} - 12q^{59} - 4q^{60} - 3q^{61} - 4q^{63} - 8q^{64} + 8q^{65} - 2q^{67} + 10q^{68} - 4q^{69} - 3q^{71} + 13q^{73} + q^{75} + 4q^{76} - 20q^{77} - 2q^{79} - 8q^{80} + q^{81} - 2q^{83} - 8q^{84} + 10q^{85} - q^{87} + 18q^{89} + 16q^{91} - 8q^{92} + 5q^{93} + 4q^{95} - 14q^{97} + 5q^{99} + O(q^{100}) \)

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 −2.00000 0 −4.00000 0 1.00000 0
\(n\): 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
\(3\) \(1\)
\(41\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(123))\).