Properties

Label 2023.2.a.b
Level $2023$
Weight $2$
Character orbit 2023.a
Self dual yes
Analytic conductor $16.154$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2023.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(16.1537363289\)
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

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

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 3.00000 −1.00000 4.00000 −3.00000 −1.00000 3.00000 6.00000 −4.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \(1\)
\(17\) \(-1\)

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 2023.2.a.b yes 1
17.b even 2 1 2023.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2023.2.a.a 1 17.b even 2 1
2023.2.a.b yes 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2023))\):

\( T_{2} + 1 \)
\( T_{3} - 3 \)

Hecke characteristic polynomials

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