Properties

Label 8033.2.a.a
Level 8033
Weight 2
Character orbit 8033.a
Self dual yes
Analytic conductor 64.144
Analytic rank 0
Dimension 1
CM no
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 8033 = 29 \cdot 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8033.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1438279437\)
Analytic rank: \(0\)
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

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

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
1.00000 1.00000 −1.00000 −3.00000 1.00000 2.00000 −3.00000 −2.00000 −3.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 8033.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8033.2.a.a 1 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(29\) \(-1\)
\(277\) \(1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8033))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - T + 2 T^{2} \)
$3$ \( 1 - T + 3 T^{2} \)
$5$ \( 1 + 3 T + 5 T^{2} \)
$7$ \( 1 - 2 T + 7 T^{2} \)
$11$ \( 1 + 3 T + 11 T^{2} \)
$13$ \( 1 - T + 13 T^{2} \)
$17$ \( 1 + 2 T + 17 T^{2} \)
$19$ \( 1 + 4 T + 19 T^{2} \)
$23$ \( 1 + 4 T + 23 T^{2} \)
$29$ \( 1 - T \)
$31$ \( 1 + 9 T + 31 T^{2} \)
$37$ \( 1 - 8 T + 37 T^{2} \)
$41$ \( 1 + 6 T + 41 T^{2} \)
$43$ \( 1 - 13 T + 43 T^{2} \)
$47$ \( 1 + 7 T + 47 T^{2} \)
$53$ \( 1 - 9 T + 53 T^{2} \)
$59$ \( 1 + 59 T^{2} \)
$61$ \( 1 - 4 T + 61 T^{2} \)
$67$ \( 1 - 2 T + 67 T^{2} \)
$71$ \( 1 + 12 T + 71 T^{2} \)
$73$ \( 1 - 14 T + 73 T^{2} \)
$79$ \( 1 - 3 T + 79 T^{2} \)
$83$ \( 1 - 10 T + 83 T^{2} \)
$89$ \( 1 + 12 T + 89 T^{2} \)
$97$ \( 1 - 14 T + 97 T^{2} \)
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