Properties

Label 201.4.a.a
Level 201
Weight 4
Character orbit 201.a
Self dual yes
Analytic conductor 11.859
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: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 201.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.8593839112\)
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

\(f(q)\) \(=\) \( q - 4q^{2} - 3q^{3} + 8q^{4} - 19q^{5} + 12q^{6} + 13q^{7} + 9q^{9} + O(q^{10}) \) \( q - 4q^{2} - 3q^{3} + 8q^{4} - 19q^{5} + 12q^{6} + 13q^{7} + 9q^{9} + 76q^{10} + 26q^{11} - 24q^{12} + 26q^{13} - 52q^{14} + 57q^{15} - 64q^{16} - 96q^{17} - 36q^{18} + 124q^{19} - 152q^{20} - 39q^{21} - 104q^{22} + 153q^{23} + 236q^{25} - 104q^{26} - 27q^{27} + 104q^{28} - 188q^{29} - 228q^{30} - 229q^{31} + 256q^{32} - 78q^{33} + 384q^{34} - 247q^{35} + 72q^{36} - 271q^{37} - 496q^{38} - 78q^{39} - 225q^{41} + 156q^{42} + 121q^{43} + 208q^{44} - 171q^{45} - 612q^{46} + 272q^{47} + 192q^{48} - 174q^{49} - 944q^{50} + 288q^{51} + 208q^{52} - 503q^{53} + 108q^{54} - 494q^{55} - 372q^{57} + 752q^{58} + 351q^{59} + 456q^{60} + 436q^{61} + 916q^{62} + 117q^{63} - 512q^{64} - 494q^{65} + 312q^{66} + 67q^{67} - 768q^{68} - 459q^{69} + 988q^{70} - 792q^{71} - 97q^{73} + 1084q^{74} - 708q^{75} + 992q^{76} + 338q^{77} + 312q^{78} - 848q^{79} + 1216q^{80} + 81q^{81} + 900q^{82} + 865q^{83} - 312q^{84} + 1824q^{85} - 484q^{86} + 564q^{87} + 430q^{89} + 684q^{90} + 338q^{91} + 1224q^{92} + 687q^{93} - 1088q^{94} - 2356q^{95} - 768q^{96} - 270q^{97} + 696q^{98} + 234q^{99} + O(q^{100}) \)

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
−4.00000 −3.00000 8.00000 −19.0000 12.0000 13.0000 0 9.00000 76.0000
\(n\): 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 201.4.a.a 1
3.b odd 2 1 603.4.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
201.4.a.a 1 1.a even 1 1 trivial
603.4.a.a 1 3.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 \( T_{2} + 4 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(201))\).

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 4 T + 8 T^{2} \)
$3$ \( 1 + 3 T \)
$5$ \( 1 + 19 T + 125 T^{2} \)
$7$ \( 1 - 13 T + 343 T^{2} \)
$11$ \( 1 - 26 T + 1331 T^{2} \)
$13$ \( 1 - 26 T + 2197 T^{2} \)
$17$ \( 1 + 96 T + 4913 T^{2} \)
$19$ \( 1 - 124 T + 6859 T^{2} \)
$23$ \( 1 - 153 T + 12167 T^{2} \)
$29$ \( 1 + 188 T + 24389 T^{2} \)
$31$ \( 1 + 229 T + 29791 T^{2} \)
$37$ \( 1 + 271 T + 50653 T^{2} \)
$41$ \( 1 + 225 T + 68921 T^{2} \)
$43$ \( 1 - 121 T + 79507 T^{2} \)
$47$ \( 1 - 272 T + 103823 T^{2} \)
$53$ \( 1 + 503 T + 148877 T^{2} \)
$59$ \( 1 - 351 T + 205379 T^{2} \)
$61$ \( 1 - 436 T + 226981 T^{2} \)
$67$ \( 1 - 67 T \)
$71$ \( 1 + 792 T + 357911 T^{2} \)
$73$ \( 1 + 97 T + 389017 T^{2} \)
$79$ \( 1 + 848 T + 493039 T^{2} \)
$83$ \( 1 - 865 T + 571787 T^{2} \)
$89$ \( 1 - 430 T + 704969 T^{2} \)
$97$ \( 1 + 270 T + 912673 T^{2} \)
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