Properties

Label 201.2.a.a
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: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{2} - q^{3} + 2q^{4} + 2q^{6} + q^{9} + O(q^{10}) \) \( q - 2q^{2} - q^{3} + 2q^{4} + 2q^{6} + q^{9} - 6q^{11} - 2q^{12} + 4q^{13} - 4q^{16} - 7q^{17} - 2q^{18} - 5q^{19} + 12q^{22} - q^{23} - 5q^{25} - 8q^{26} - q^{27} + q^{29} - 4q^{31} + 8q^{32} + 6q^{33} + 14q^{34} + 2q^{36} + 3q^{37} + 10q^{38} - 4q^{39} - 6q^{43} - 12q^{44} + 2q^{46} + 9q^{47} + 4q^{48} - 7q^{49} + 10q^{50} + 7q^{51} + 8q^{52} + 10q^{53} + 2q^{54} + 5q^{57} - 2q^{58} + 3q^{59} + 2q^{61} + 8q^{62} - 8q^{64} - 12q^{66} - q^{67} - 14q^{68} + q^{69} - 16q^{71} - 7q^{73} - 6q^{74} + 5q^{75} - 10q^{76} + 8q^{78} + 8q^{79} + q^{81} - 4q^{83} + 12q^{86} - q^{87} - 15q^{89} - 2q^{92} + 4q^{93} - 18q^{94} - 8q^{96} + 4q^{97} + 14q^{98} - 6q^{99} + O(q^{100}) \)

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 0 2.00000 0 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.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 201.2.a.a 1
3.b odd 2 1 603.2.a.f 1
4.b odd 2 1 3216.2.a.j 1
5.b even 2 1 5025.2.a.i 1
7.b odd 2 1 9849.2.a.b 1
12.b even 2 1 9648.2.a.j 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
201.2.a.a 1 1.a even 1 1 trivial
603.2.a.f 1 3.b odd 2 1
3216.2.a.j 1 4.b odd 2 1
5025.2.a.i 1 5.b even 2 1
9648.2.a.j 1 12.b even 2 1
9849.2.a.b 1 7.b odd 2 1

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(67\) \(1\)

Hecke kernels

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

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T + 2 T^{2} \)
$3$ \( 1 + T \)
$5$ \( 1 + 5 T^{2} \)
$7$ \( 1 + 7 T^{2} \)
$11$ \( 1 + 6 T + 11 T^{2} \)
$13$ \( 1 - 4 T + 13 T^{2} \)
$17$ \( 1 + 7 T + 17 T^{2} \)
$19$ \( 1 + 5 T + 19 T^{2} \)
$23$ \( 1 + T + 23 T^{2} \)
$29$ \( 1 - T + 29 T^{2} \)
$31$ \( 1 + 4 T + 31 T^{2} \)
$37$ \( 1 - 3 T + 37 T^{2} \)
$41$ \( 1 + 41 T^{2} \)
$43$ \( 1 + 6 T + 43 T^{2} \)
$47$ \( 1 - 9 T + 47 T^{2} \)
$53$ \( 1 - 10 T + 53 T^{2} \)
$59$ \( 1 - 3 T + 59 T^{2} \)
$61$ \( 1 - 2 T + 61 T^{2} \)
$67$ \( 1 + T \)
$71$ \( 1 + 16 T + 71 T^{2} \)
$73$ \( 1 + 7 T + 73 T^{2} \)
$79$ \( 1 - 8 T + 79 T^{2} \)
$83$ \( 1 + 4 T + 83 T^{2} \)
$89$ \( 1 + 15 T + 89 T^{2} \)
$97$ \( 1 - 4 T + 97 T^{2} \)
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