Properties

Label 61.2.a.a
Level 61
Weight 2
Character orbit 61.a
Self dual Yes
Analytic conductor 0.487
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 61.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.48708745233\)
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

\(f(q)\) \(=\) \( q - q^{2} - 2q^{3} - q^{4} - 3q^{5} + 2q^{6} + q^{7} + 3q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - 2q^{3} - q^{4} - 3q^{5} + 2q^{6} + q^{7} + 3q^{8} + q^{9} + 3q^{10} - 5q^{11} + 2q^{12} + q^{13} - q^{14} + 6q^{15} - q^{16} + 4q^{17} - q^{18} - 4q^{19} + 3q^{20} - 2q^{21} + 5q^{22} - 9q^{23} - 6q^{24} + 4q^{25} - q^{26} + 4q^{27} - q^{28} - 6q^{29} - 6q^{30} - 5q^{32} + 10q^{33} - 4q^{34} - 3q^{35} - q^{36} + 8q^{37} + 4q^{38} - 2q^{39} - 9q^{40} + 5q^{41} + 2q^{42} - 8q^{43} + 5q^{44} - 3q^{45} + 9q^{46} + 4q^{47} + 2q^{48} - 6q^{49} - 4q^{50} - 8q^{51} - q^{52} + 6q^{53} - 4q^{54} + 15q^{55} + 3q^{56} + 8q^{57} + 6q^{58} + 9q^{59} - 6q^{60} - q^{61} + q^{63} + 7q^{64} - 3q^{65} - 10q^{66} - 7q^{67} - 4q^{68} + 18q^{69} + 3q^{70} - 8q^{71} + 3q^{72} - 11q^{73} - 8q^{74} - 8q^{75} + 4q^{76} - 5q^{77} + 2q^{78} + 3q^{79} + 3q^{80} - 11q^{81} - 5q^{82} + 4q^{83} + 2q^{84} - 12q^{85} + 8q^{86} + 12q^{87} - 15q^{88} - 4q^{89} + 3q^{90} + q^{91} + 9q^{92} - 4q^{94} + 12q^{95} + 10q^{96} - 14q^{97} + 6q^{98} - 5q^{99} + O(q^{100}) \)

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
−1.00000 −2.00000 −1.00000 −3.00000 2.00000 1.00000 3.00000 1.00000 3.00000
\(n\): 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
\(61\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} + 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(61))\).