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

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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

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

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 −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 \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\).