Properties

Label 5.6.a.a
Level 5
Weight 6
Character orbit 5.a
Self dual Yes
Analytic conductor 0.802
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 5.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.801919099065\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q + 2q^{2} - 4q^{3} - 28q^{4} + 25q^{5} - 8q^{6} + 192q^{7} - 120q^{8} - 227q^{9} + O(q^{10}) \) \( q + 2q^{2} - 4q^{3} - 28q^{4} + 25q^{5} - 8q^{6} + 192q^{7} - 120q^{8} - 227q^{9} + 50q^{10} - 148q^{11} + 112q^{12} + 286q^{13} + 384q^{14} - 100q^{15} + 656q^{16} - 1678q^{17} - 454q^{18} + 1060q^{19} - 700q^{20} - 768q^{21} - 296q^{22} + 2976q^{23} + 480q^{24} + 625q^{25} + 572q^{26} + 1880q^{27} - 5376q^{28} - 3410q^{29} - 200q^{30} - 2448q^{31} + 5152q^{32} + 592q^{33} - 3356q^{34} + 4800q^{35} + 6356q^{36} + 182q^{37} + 2120q^{38} - 1144q^{39} - 3000q^{40} - 9398q^{41} - 1536q^{42} - 1244q^{43} + 4144q^{44} - 5675q^{45} + 5952q^{46} - 12088q^{47} - 2624q^{48} + 20057q^{49} + 1250q^{50} + 6712q^{51} - 8008q^{52} + 23846q^{53} + 3760q^{54} - 3700q^{55} - 23040q^{56} - 4240q^{57} - 6820q^{58} - 20020q^{59} + 2800q^{60} + 32302q^{61} - 4896q^{62} - 43584q^{63} - 10688q^{64} + 7150q^{65} + 1184q^{66} + 60972q^{67} + 46984q^{68} - 11904q^{69} + 9600q^{70} - 32648q^{71} + 27240q^{72} - 38774q^{73} + 364q^{74} - 2500q^{75} - 29680q^{76} - 28416q^{77} - 2288q^{78} - 33360q^{79} + 16400q^{80} + 47641q^{81} - 18796q^{82} + 16716q^{83} + 21504q^{84} - 41950q^{85} - 2488q^{86} + 13640q^{87} + 17760q^{88} + 101370q^{89} - 11350q^{90} + 54912q^{91} - 83328q^{92} + 9792q^{93} - 24176q^{94} + 26500q^{95} - 20608q^{96} - 119038q^{97} + 40114q^{98} + 33596q^{99} + O(q^{100}) \)

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 −4.00000 −28.0000 25.0000 −8.00000 192.000 −120.000 −227.000 50.0000
\(n\): 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
\(5\) \(-1\)

Hecke kernels

There are no other newforms in \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\).