Properties

Label 201.3.b.a
Level 201
Weight 3
Character orbit 201.b
Analytic conductor 5.477
Analytic rank 0
Dimension 22
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 201 = 3 \cdot 67 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 201.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.47685331364\)
Analytic rank: \(0\)
Dimension: \(22\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 22q - 52q^{4} - 66q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 22q - 52q^{4} - 66q^{9} - 36q^{10} + 72q^{14} + 12q^{15} + 116q^{16} - 14q^{17} - 26q^{19} + 48q^{21} + 32q^{22} - 82q^{23} + 36q^{24} - 62q^{25} - 100q^{26} + 102q^{29} + 36q^{33} - 180q^{35} + 156q^{36} + 106q^{37} - 72q^{39} + 76q^{40} + 154q^{47} + 146q^{49} - 224q^{55} - 452q^{56} + 370q^{59} - 24q^{60} - 300q^{62} + 148q^{64} - 284q^{65} - 134q^{67} - 116q^{68} + 160q^{71} + 218q^{73} + 480q^{76} - 396q^{77} + 198q^{81} - 68q^{82} + 128q^{83} + 20q^{86} - 856q^{88} - 118q^{89} + 108q^{90} - 400q^{91} + 804q^{92} - 72q^{93} - 144q^{96} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
133.1 3.81177i 1.73205i −10.5296 6.86815i −6.60217 3.56836i 24.8892i −3.00000 −26.1798
133.2 3.60849i 1.73205i −9.02122 2.97147i 6.25009 2.36023i 18.1190i −3.00000 10.7225
133.3 3.21711i 1.73205i −6.34981 8.83855i −5.57220 10.0054i 7.55961i −3.00000 28.4346
133.4 3.12361i 1.73205i −5.75692 8.39184i 5.41025 3.67092i 5.48792i −3.00000 −26.2128
133.5 2.88392i 1.73205i −4.31697 1.18875i 4.99509 3.84699i 0.914116i −3.00000 3.42825
133.6 2.74898i 1.73205i −3.55688 0.569953i −4.76137 7.88425i 1.21813i −3.00000 −1.56679
133.7 1.70381i 1.73205i 1.09704 1.67394i −2.95108 0.231323i 8.68437i −3.00000 2.85207
133.8 1.30530i 1.73205i 2.29618 2.19844i 2.26085 9.13473i 8.21843i −3.00000 2.86963
133.9 0.952997i 1.73205i 3.09180 5.09554i 1.65064 5.68326i 6.75846i −3.00000 −4.85603
133.10 0.858352i 1.73205i 3.26323 8.02842i −1.48671 1.82241i 6.23441i −3.00000 −6.89121
133.11 0.465702i 1.73205i 3.78312 1.28941i 0.806619 11.7488i 3.62461i −3.00000 −0.600481
133.12 0.465702i 1.73205i 3.78312 1.28941i 0.806619 11.7488i 3.62461i −3.00000 −0.600481
133.13 0.858352i 1.73205i 3.26323 8.02842i −1.48671 1.82241i 6.23441i −3.00000 −6.89121
133.14 0.952997i 1.73205i 3.09180 5.09554i 1.65064 5.68326i 6.75846i −3.00000 −4.85603
133.15 1.30530i 1.73205i 2.29618 2.19844i 2.26085 9.13473i 8.21843i −3.00000 2.86963
133.16 1.70381i 1.73205i 1.09704 1.67394i −2.95108 0.231323i 8.68437i −3.00000 2.85207
133.17 2.74898i 1.73205i −3.55688 0.569953i −4.76137 7.88425i 1.21813i −3.00000 −1.56679
133.18 2.88392i 1.73205i −4.31697 1.18875i 4.99509 3.84699i 0.914116i −3.00000 3.42825
133.19 3.12361i 1.73205i −5.75692 8.39184i 5.41025 3.67092i 5.48792i −3.00000 −26.2128
133.20 3.21711i 1.73205i −6.34981 8.83855i −5.57220 10.0054i 7.55961i −3.00000 28.4346
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 133.22
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
67.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 201.3.b.a 22
3.b odd 2 1 603.3.b.e 22
67.b odd 2 1 inner 201.3.b.a 22
201.d even 2 1 603.3.b.e 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
201.3.b.a 22 1.a even 1 1 trivial
201.3.b.a 22 67.b odd 2 1 inner
603.3.b.e 22 3.b odd 2 1
603.3.b.e 22 201.d even 2 1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(201, [\chi])\).

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database