Properties

Label 121.2.a.d
Level 121
Weight 2
Character orbit 121.a
Self dual Yes
Analytic conductor 0.966
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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: \(0\)
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

\(f(q)\) \(=\) \( q + 2q^{2} - q^{3} + 2q^{4} + q^{5} - 2q^{6} + 2q^{7} - 2q^{9} + O(q^{10}) \) \( q + 2q^{2} - q^{3} + 2q^{4} + q^{5} - 2q^{6} + 2q^{7} - 2q^{9} + 2q^{10} - 2q^{12} - 4q^{13} + 4q^{14} - q^{15} - 4q^{16} + 2q^{17} - 4q^{18} + 2q^{20} - 2q^{21} - q^{23} - 4q^{25} - 8q^{26} + 5q^{27} + 4q^{28} - 2q^{30} + 7q^{31} - 8q^{32} + 4q^{34} + 2q^{35} - 4q^{36} + 3q^{37} + 4q^{39} + 8q^{41} - 4q^{42} + 6q^{43} - 2q^{45} - 2q^{46} + 8q^{47} + 4q^{48} - 3q^{49} - 8q^{50} - 2q^{51} - 8q^{52} - 6q^{53} + 10q^{54} + 5q^{59} - 2q^{60} - 12q^{61} + 14q^{62} - 4q^{63} - 8q^{64} - 4q^{65} - 7q^{67} + 4q^{68} + q^{69} + 4q^{70} - 3q^{71} - 4q^{73} + 6q^{74} + 4q^{75} + 8q^{78} + 10q^{79} - 4q^{80} + q^{81} + 16q^{82} + 6q^{83} - 4q^{84} + 2q^{85} + 12q^{86} + 15q^{89} - 4q^{90} - 8q^{91} - 2q^{92} - 7q^{93} + 16q^{94} + 8q^{96} - 7q^{97} - 6q^{98} + O(q^{100}) \)

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
2.00000 −1.00000 2.00000 1.00000 −2.00000 2.00000 0 −2.00000 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
\(11\) \(-1\)

Hecke kernels

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