Properties

Label 10.4.a.a
Level 10
Weight 4
Character orbit 10.a
Self dual Yes
Analytic conductor 0.590
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 10.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.590019100057\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut 37q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut 37q^{9} \) \(\mathstrut +\mathstrut 10q^{10} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 32q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut -\mathstrut 40q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut +\mathstrut 66q^{17} \) \(\mathstrut +\mathstrut 74q^{18} \) \(\mathstrut -\mathstrut 100q^{19} \) \(\mathstrut +\mathstrut 20q^{20} \) \(\mathstrut +\mathstrut 32q^{21} \) \(\mathstrut +\mathstrut 24q^{22} \) \(\mathstrut +\mathstrut 132q^{23} \) \(\mathstrut -\mathstrut 64q^{24} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 116q^{26} \) \(\mathstrut -\mathstrut 80q^{27} \) \(\mathstrut -\mathstrut 16q^{28} \) \(\mathstrut -\mathstrut 90q^{29} \) \(\mathstrut -\mathstrut 80q^{30} \) \(\mathstrut +\mathstrut 152q^{31} \) \(\mathstrut +\mathstrut 32q^{32} \) \(\mathstrut -\mathstrut 96q^{33} \) \(\mathstrut +\mathstrut 132q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 148q^{36} \) \(\mathstrut -\mathstrut 34q^{37} \) \(\mathstrut -\mathstrut 200q^{38} \) \(\mathstrut +\mathstrut 464q^{39} \) \(\mathstrut +\mathstrut 40q^{40} \) \(\mathstrut -\mathstrut 438q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut +\mathstrut 32q^{43} \) \(\mathstrut +\mathstrut 48q^{44} \) \(\mathstrut +\mathstrut 185q^{45} \) \(\mathstrut +\mathstrut 264q^{46} \) \(\mathstrut -\mathstrut 204q^{47} \) \(\mathstrut -\mathstrut 128q^{48} \) \(\mathstrut -\mathstrut 327q^{49} \) \(\mathstrut +\mathstrut 50q^{50} \) \(\mathstrut -\mathstrut 528q^{51} \) \(\mathstrut -\mathstrut 232q^{52} \) \(\mathstrut +\mathstrut 222q^{53} \) \(\mathstrut -\mathstrut 160q^{54} \) \(\mathstrut +\mathstrut 60q^{55} \) \(\mathstrut -\mathstrut 32q^{56} \) \(\mathstrut +\mathstrut 800q^{57} \) \(\mathstrut -\mathstrut 180q^{58} \) \(\mathstrut +\mathstrut 420q^{59} \) \(\mathstrut -\mathstrut 160q^{60} \) \(\mathstrut +\mathstrut 902q^{61} \) \(\mathstrut +\mathstrut 304q^{62} \) \(\mathstrut -\mathstrut 148q^{63} \) \(\mathstrut +\mathstrut 64q^{64} \) \(\mathstrut -\mathstrut 290q^{65} \) \(\mathstrut -\mathstrut 192q^{66} \) \(\mathstrut -\mathstrut 1024q^{67} \) \(\mathstrut +\mathstrut 264q^{68} \) \(\mathstrut -\mathstrut 1056q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut +\mathstrut 432q^{71} \) \(\mathstrut +\mathstrut 296q^{72} \) \(\mathstrut +\mathstrut 362q^{73} \) \(\mathstrut -\mathstrut 68q^{74} \) \(\mathstrut -\mathstrut 200q^{75} \) \(\mathstrut -\mathstrut 400q^{76} \) \(\mathstrut -\mathstrut 48q^{77} \) \(\mathstrut +\mathstrut 928q^{78} \) \(\mathstrut -\mathstrut 160q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut -\mathstrut 359q^{81} \) \(\mathstrut -\mathstrut 876q^{82} \) \(\mathstrut +\mathstrut 72q^{83} \) \(\mathstrut +\mathstrut 128q^{84} \) \(\mathstrut +\mathstrut 330q^{85} \) \(\mathstrut +\mathstrut 64q^{86} \) \(\mathstrut +\mathstrut 720q^{87} \) \(\mathstrut +\mathstrut 96q^{88} \) \(\mathstrut +\mathstrut 810q^{89} \) \(\mathstrut +\mathstrut 370q^{90} \) \(\mathstrut +\mathstrut 232q^{91} \) \(\mathstrut +\mathstrut 528q^{92} \) \(\mathstrut -\mathstrut 1216q^{93} \) \(\mathstrut -\mathstrut 408q^{94} \) \(\mathstrut -\mathstrut 500q^{95} \) \(\mathstrut -\mathstrut 256q^{96} \) \(\mathstrut +\mathstrut 1106q^{97} \) \(\mathstrut -\mathstrut 654q^{98} \) \(\mathstrut +\mathstrut 444q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −8.00000 4.00000 5.00000 −16.0000 −4.00000 8.00000 37.0000 10.0000
\(n\): 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
\(2\) \(-1\)
\(5\) \(-1\)

Hecke kernels

There are no other newforms in \(S_{4}^{\mathrm{new}}(\Gamma_0(10))\).