Properties

Label 2023.4.a.b
Level $2023$
Weight $4$
Character orbit 2023.a
Self dual yes
Analytic conductor $119.361$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2023.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(119.360863942\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 119)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + 6q^{3} - 7q^{4} + 20q^{5} - 6q^{6} + 7q^{7} + 15q^{8} + 9q^{9} + O(q^{10}) \) \( q - q^{2} + 6q^{3} - 7q^{4} + 20q^{5} - 6q^{6} + 7q^{7} + 15q^{8} + 9q^{9} - 20q^{10} - 60q^{11} - 42q^{12} - 68q^{13} - 7q^{14} + 120q^{15} + 41q^{16} - 9q^{18} - 70q^{19} - 140q^{20} + 42q^{21} + 60q^{22} + 176q^{23} + 90q^{24} + 275q^{25} + 68q^{26} - 108q^{27} - 49q^{28} + 90q^{29} - 120q^{30} - 196q^{31} - 161q^{32} - 360q^{33} + 140q^{35} - 63q^{36} - 22q^{37} + 70q^{38} - 408q^{39} + 300q^{40} + 138q^{41} - 42q^{42} + 328q^{43} + 420q^{44} + 180q^{45} - 176q^{46} - 12q^{47} + 246q^{48} + 49q^{49} - 275q^{50} + 476q^{52} - 234q^{53} + 108q^{54} - 1200q^{55} + 105q^{56} - 420q^{57} - 90q^{58} - 54q^{59} - 840q^{60} - 44q^{61} + 196q^{62} + 63q^{63} - 167q^{64} - 1360q^{65} + 360q^{66} - 596q^{67} + 1056q^{69} - 140q^{70} - 200q^{71} + 135q^{72} - 1122q^{73} + 22q^{74} + 1650q^{75} + 490q^{76} - 420q^{77} + 408q^{78} - 480q^{79} + 820q^{80} - 891q^{81} - 138q^{82} - 838q^{83} - 294q^{84} - 328q^{86} + 540q^{87} - 900q^{88} + 778q^{89} - 180q^{90} - 476q^{91} - 1232q^{92} - 1176q^{93} + 12q^{94} - 1400q^{95} - 966q^{96} - 1142q^{97} - 49q^{98} - 540q^{99} + O(q^{100}) \)

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 6.00000 −7.00000 20.0000 −6.00000 7.00000 15.0000 9.00000 −20.0000
\(n\): 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 2023.4.a.b 1
17.b even 2 1 119.4.a.a 1
51.c odd 2 1 1071.4.a.b 1
68.d odd 2 1 1904.4.a.a 1
119.d odd 2 1 833.4.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
119.4.a.a 1 17.b even 2 1
833.4.a.b 1 119.d odd 2 1
1071.4.a.b 1 51.c odd 2 1
1904.4.a.a 1 68.d odd 2 1
2023.4.a.b 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(2023))\):

\( T_{2} + 1 \)
\( T_{3} - 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( -6 + T \)
$5$ \( -20 + T \)
$7$ \( -7 + T \)
$11$ \( 60 + T \)
$13$ \( 68 + T \)
$17$ \( T \)
$19$ \( 70 + T \)
$23$ \( -176 + T \)
$29$ \( -90 + T \)
$31$ \( 196 + T \)
$37$ \( 22 + T \)
$41$ \( -138 + T \)
$43$ \( -328 + T \)
$47$ \( 12 + T \)
$53$ \( 234 + T \)
$59$ \( 54 + T \)
$61$ \( 44 + T \)
$67$ \( 596 + T \)
$71$ \( 200 + T \)
$73$ \( 1122 + T \)
$79$ \( 480 + T \)
$83$ \( 838 + T \)
$89$ \( -778 + T \)
$97$ \( 1142 + T \)
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