Properties

Label 23.4.a.a
Level 23
Weight 4
Character orbit 23.a
Self dual yes
Analytic conductor 1.357
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 23.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.35704393013\)
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

\(f(q)\) \(=\) \( q - 2q^{2} - 5q^{3} - 4q^{4} - 6q^{5} + 10q^{6} - 8q^{7} + 24q^{8} - 2q^{9} + O(q^{10}) \) \( q - 2q^{2} - 5q^{3} - 4q^{4} - 6q^{5} + 10q^{6} - 8q^{7} + 24q^{8} - 2q^{9} + 12q^{10} + 34q^{11} + 20q^{12} - 57q^{13} + 16q^{14} + 30q^{15} - 16q^{16} - 80q^{17} + 4q^{18} - 70q^{19} + 24q^{20} + 40q^{21} - 68q^{22} + 23q^{23} - 120q^{24} - 89q^{25} + 114q^{26} + 145q^{27} + 32q^{28} + 245q^{29} - 60q^{30} + 103q^{31} - 160q^{32} - 170q^{33} + 160q^{34} + 48q^{35} + 8q^{36} - 298q^{37} + 140q^{38} + 285q^{39} - 144q^{40} + 95q^{41} - 80q^{42} + 88q^{43} - 136q^{44} + 12q^{45} - 46q^{46} - 357q^{47} + 80q^{48} - 279q^{49} + 178q^{50} + 400q^{51} + 228q^{52} - 414q^{53} - 290q^{54} - 204q^{55} - 192q^{56} + 350q^{57} - 490q^{58} - 408q^{59} - 120q^{60} + 822q^{61} - 206q^{62} + 16q^{63} + 448q^{64} + 342q^{65} + 340q^{66} + 926q^{67} + 320q^{68} - 115q^{69} - 96q^{70} + 335q^{71} - 48q^{72} - 899q^{73} + 596q^{74} + 445q^{75} + 280q^{76} - 272q^{77} - 570q^{78} - 1322q^{79} + 96q^{80} - 671q^{81} - 190q^{82} - 36q^{83} - 160q^{84} + 480q^{85} - 176q^{86} - 1225q^{87} + 816q^{88} - 460q^{89} - 24q^{90} + 456q^{91} - 92q^{92} - 515q^{93} + 714q^{94} + 420q^{95} + 800q^{96} - 964q^{97} + 558q^{98} - 68q^{99} + O(q^{100}) \)

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
−2.00000 −5.00000 −4.00000 −6.00000 10.0000 −8.00000 24.0000 −2.00000 12.0000
\(n\): 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 23.4.a.a 1
3.b odd 2 1 207.4.a.a 1
4.b odd 2 1 368.4.a.d 1
5.b even 2 1 575.4.a.g 1
5.c odd 4 2 575.4.b.b 2
7.b odd 2 1 1127.4.a.a 1
8.b even 2 1 1472.4.a.h 1
8.d odd 2 1 1472.4.a.c 1
23.b odd 2 1 529.4.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
23.4.a.a 1 1.a even 1 1 trivial
207.4.a.a 1 3.b odd 2 1
368.4.a.d 1 4.b odd 2 1
529.4.a.a 1 23.b odd 2 1
575.4.a.g 1 5.b even 2 1
575.4.b.b 2 5.c odd 4 2
1127.4.a.a 1 7.b odd 2 1
1472.4.a.c 1 8.d odd 2 1
1472.4.a.h 1 8.b even 2 1

Atkin-Lehner signs

\( p \) Sign
\(23\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} + 2 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(23))\).

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T + 8 T^{2} \)
$3$ \( 1 + 5 T + 27 T^{2} \)
$5$ \( 1 + 6 T + 125 T^{2} \)
$7$ \( 1 + 8 T + 343 T^{2} \)
$11$ \( 1 - 34 T + 1331 T^{2} \)
$13$ \( 1 + 57 T + 2197 T^{2} \)
$17$ \( 1 + 80 T + 4913 T^{2} \)
$19$ \( 1 + 70 T + 6859 T^{2} \)
$23$ \( 1 - 23 T \)
$29$ \( 1 - 245 T + 24389 T^{2} \)
$31$ \( 1 - 103 T + 29791 T^{2} \)
$37$ \( 1 + 298 T + 50653 T^{2} \)
$41$ \( 1 - 95 T + 68921 T^{2} \)
$43$ \( 1 - 88 T + 79507 T^{2} \)
$47$ \( 1 + 357 T + 103823 T^{2} \)
$53$ \( 1 + 414 T + 148877 T^{2} \)
$59$ \( 1 + 408 T + 205379 T^{2} \)
$61$ \( 1 - 822 T + 226981 T^{2} \)
$67$ \( 1 - 926 T + 300763 T^{2} \)
$71$ \( 1 - 335 T + 357911 T^{2} \)
$73$ \( 1 + 899 T + 389017 T^{2} \)
$79$ \( 1 + 1322 T + 493039 T^{2} \)
$83$ \( 1 + 36 T + 571787 T^{2} \)
$89$ \( 1 + 460 T + 704969 T^{2} \)
$97$ \( 1 + 964 T + 912673 T^{2} \)
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