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

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

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:

Atkin-Lehner signs

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

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 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

Hecke kernels

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 2 \) Copy content Toggle raw display
$3$ \( T + 5 \) Copy content Toggle raw display
$5$ \( T + 6 \) Copy content Toggle raw display
$7$ \( T + 8 \) Copy content Toggle raw display
$11$ \( T - 34 \) Copy content Toggle raw display
$13$ \( T + 57 \) Copy content Toggle raw display
$17$ \( T + 80 \) Copy content Toggle raw display
$19$ \( T + 70 \) Copy content Toggle raw display
$23$ \( T - 23 \) Copy content Toggle raw display
$29$ \( T - 245 \) Copy content Toggle raw display
$31$ \( T - 103 \) Copy content Toggle raw display
$37$ \( T + 298 \) Copy content Toggle raw display
$41$ \( T - 95 \) Copy content Toggle raw display
$43$ \( T - 88 \) Copy content Toggle raw display
$47$ \( T + 357 \) Copy content Toggle raw display
$53$ \( T + 414 \) Copy content Toggle raw display
$59$ \( T + 408 \) Copy content Toggle raw display
$61$ \( T - 822 \) Copy content Toggle raw display
$67$ \( T - 926 \) Copy content Toggle raw display
$71$ \( T - 335 \) Copy content Toggle raw display
$73$ \( T + 899 \) Copy content Toggle raw display
$79$ \( T + 1322 \) Copy content Toggle raw display
$83$ \( T + 36 \) Copy content Toggle raw display
$89$ \( T + 460 \) Copy content Toggle raw display
$97$ \( T + 964 \) Copy content Toggle raw display
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