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

$q$-expansion

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

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.

Atkin-Lehner signs

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

Hecke kernels

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