Properties

Label 201.2.a.b
Level 201
Weight 2
Character orbit 201.a
Self dual Yes
Analytic conductor 1.605
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 201 = 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 201.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.60499308063\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} - 5q^{7} + 3q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} - 5q^{7} + 3q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} - 4q^{13} + 5q^{14} - q^{15} - q^{16} + 6q^{17} - q^{18} - 2q^{19} + q^{20} - 5q^{21} + 4q^{22} - 3q^{23} + 3q^{24} - 4q^{25} + 4q^{26} + q^{27} + 5q^{28} + 4q^{29} + q^{30} - 7q^{31} - 5q^{32} - 4q^{33} - 6q^{34} + 5q^{35} - q^{36} + 5q^{37} + 2q^{38} - 4q^{39} - 3q^{40} - 3q^{41} + 5q^{42} + 7q^{43} + 4q^{44} - q^{45} + 3q^{46} + 8q^{47} - q^{48} + 18q^{49} + 4q^{50} + 6q^{51} + 4q^{52} - 5q^{53} - q^{54} + 4q^{55} - 15q^{56} - 2q^{57} - 4q^{58} + 3q^{59} + q^{60} - 2q^{61} + 7q^{62} - 5q^{63} + 7q^{64} + 4q^{65} + 4q^{66} + q^{67} - 6q^{68} - 3q^{69} - 5q^{70} - 12q^{71} + 3q^{72} - 13q^{73} - 5q^{74} - 4q^{75} + 2q^{76} + 20q^{77} + 4q^{78} - 8q^{79} + q^{80} + q^{81} + 3q^{82} + q^{83} + 5q^{84} - 6q^{85} - 7q^{86} + 4q^{87} - 12q^{88} + 4q^{89} + q^{90} + 20q^{91} + 3q^{92} - 7q^{93} - 8q^{94} + 2q^{95} - 5q^{96} - 12q^{97} - 18q^{98} - 4q^{99} + O(q^{100}) \)

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 1.00000 −1.00000 −1.00000 −1.00000 −5.00000 3.00000 1.00000 1.00000
\(n\): 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
\(3\) \(-1\)
\(67\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} + 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(201))\).