Properties

Label 123.2.a.a
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

\(f(q)\) \(=\) \( q - 2q^{2} + q^{3} + 2q^{4} - 4q^{5} - 2q^{6} - 2q^{7} + q^{9} + O(q^{10}) \) \( q - 2q^{2} + q^{3} + 2q^{4} - 4q^{5} - 2q^{6} - 2q^{7} + q^{9} + 8q^{10} - 3q^{11} + 2q^{12} - 6q^{13} + 4q^{14} - 4q^{15} - 4q^{16} + 3q^{17} - 2q^{18} - 8q^{20} - 2q^{21} + 6q^{22} - 6q^{23} + 11q^{25} + 12q^{26} + q^{27} - 4q^{28} + 5q^{29} + 8q^{30} + 7q^{31} + 8q^{32} - 3q^{33} - 6q^{34} + 8q^{35} + 2q^{36} - 7q^{37} - 6q^{39} + q^{41} + 4q^{42} - q^{43} - 6q^{44} - 4q^{45} + 12q^{46} + 3q^{47} - 4q^{48} - 3q^{49} - 22q^{50} + 3q^{51} - 12q^{52} - 6q^{53} - 2q^{54} + 12q^{55} - 10q^{58} - 8q^{60} - 3q^{61} - 14q^{62} - 2q^{63} - 8q^{64} + 24q^{65} + 6q^{66} - 2q^{67} + 6q^{68} - 6q^{69} - 16q^{70} - 3q^{71} - 11q^{73} + 14q^{74} + 11q^{75} + 6q^{77} + 12q^{78} + 10q^{79} + 16q^{80} + q^{81} - 2q^{82} - 16q^{83} - 4q^{84} - 12q^{85} + 2q^{86} + 5q^{87} - 10q^{89} + 8q^{90} + 12q^{91} - 12q^{92} + 7q^{93} - 6q^{94} + 8q^{96} - 12q^{97} + 6q^{98} - 3q^{99} + O(q^{100}) \)

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
−2.00000 1.00000 2.00000 −4.00000 −2.00000 −2.00000 0 1.00000 8.00000
\(n\): 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
\(3\) \(-1\)
\(41\) \(-1\)

Hecke kernels

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