Properties

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

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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 7)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + 2q^{3} - 7q^{4} - 16q^{5} - 2q^{6} + 7q^{7} + 15q^{8} - 23q^{9} + O(q^{10}) \) \( q - q^{2} + 2q^{3} - 7q^{4} - 16q^{5} - 2q^{6} + 7q^{7} + 15q^{8} - 23q^{9} + 16q^{10} + 8q^{11} - 14q^{12} + 28q^{13} - 7q^{14} - 32q^{15} + 41q^{16} + 23q^{18} - 110q^{19} + 112q^{20} + 14q^{21} - 8q^{22} - 48q^{23} + 30q^{24} + 131q^{25} - 28q^{26} - 100q^{27} - 49q^{28} + 110q^{29} + 32q^{30} - 12q^{31} - 161q^{32} + 16q^{33} - 112q^{35} + 161q^{36} + 246q^{37} + 110q^{38} + 56q^{39} - 240q^{40} - 182q^{41} - 14q^{42} + 128q^{43} - 56q^{44} + 368q^{45} + 48q^{46} + 324q^{47} + 82q^{48} + 49q^{49} - 131q^{50} - 196q^{52} - 162q^{53} + 100q^{54} - 128q^{55} + 105q^{56} - 220q^{57} - 110q^{58} + 810q^{59} + 224q^{60} + 488q^{61} + 12q^{62} - 161q^{63} - 167q^{64} - 448q^{65} - 16q^{66} + 244q^{67} - 96q^{69} + 112q^{70} + 768q^{71} - 345q^{72} + 702q^{73} - 246q^{74} + 262q^{75} + 770q^{76} + 56q^{77} - 56q^{78} - 440q^{79} - 656q^{80} + 421q^{81} + 182q^{82} - 1302q^{83} - 98q^{84} - 128q^{86} + 220q^{87} + 120q^{88} + 730q^{89} - 368q^{90} + 196q^{91} + 336q^{92} - 24q^{93} - 324q^{94} + 1760q^{95} - 322q^{96} - 294q^{97} - 49q^{98} - 184q^{99} + O(q^{100}) \)

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 2.00000 −7.00000 −16.0000 −2.00000 7.00000 15.0000 −23.0000 16.0000
\(n\): 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.a 1
17.b even 2 1 7.4.a.a 1
51.c odd 2 1 63.4.a.b 1
68.d odd 2 1 112.4.a.f 1
85.c even 2 1 175.4.a.b 1
85.g odd 4 2 175.4.b.b 2
119.d odd 2 1 49.4.a.b 1
119.h odd 6 2 49.4.c.b 2
119.j even 6 2 49.4.c.c 2
136.e odd 2 1 448.4.a.e 1
136.h even 2 1 448.4.a.i 1
187.b odd 2 1 847.4.a.b 1
204.h even 2 1 1008.4.a.c 1
221.b even 2 1 1183.4.a.b 1
255.h odd 2 1 1575.4.a.e 1
357.c even 2 1 441.4.a.i 1
357.q odd 6 2 441.4.e.h 2
357.s even 6 2 441.4.e.e 2
476.e even 2 1 784.4.a.g 1
595.b odd 2 1 1225.4.a.j 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
7.4.a.a 1 17.b even 2 1
49.4.a.b 1 119.d odd 2 1
49.4.c.b 2 119.h odd 6 2
49.4.c.c 2 119.j even 6 2
63.4.a.b 1 51.c odd 2 1
112.4.a.f 1 68.d odd 2 1
175.4.a.b 1 85.c even 2 1
175.4.b.b 2 85.g odd 4 2
441.4.a.i 1 357.c even 2 1
441.4.e.e 2 357.s even 6 2
441.4.e.h 2 357.q odd 6 2
448.4.a.e 1 136.e odd 2 1
448.4.a.i 1 136.h even 2 1
784.4.a.g 1 476.e even 2 1
847.4.a.b 1 187.b odd 2 1
1008.4.a.c 1 204.h even 2 1
1183.4.a.b 1 221.b even 2 1
1225.4.a.j 1 595.b odd 2 1
1575.4.a.e 1 255.h odd 2 1
2023.4.a.a 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(2023))\):

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( -2 + T \)
$5$ \( 16 + T \)
$7$ \( -7 + T \)
$11$ \( -8 + T \)
$13$ \( -28 + T \)
$17$ \( T \)
$19$ \( 110 + T \)
$23$ \( 48 + T \)
$29$ \( -110 + T \)
$31$ \( 12 + T \)
$37$ \( -246 + T \)
$41$ \( 182 + T \)
$43$ \( -128 + T \)
$47$ \( -324 + T \)
$53$ \( 162 + T \)
$59$ \( -810 + T \)
$61$ \( -488 + T \)
$67$ \( -244 + T \)
$71$ \( -768 + T \)
$73$ \( -702 + T \)
$79$ \( 440 + T \)
$83$ \( 1302 + T \)
$89$ \( -730 + T \)
$97$ \( 294 + T \)
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