Properties

Label 6.10.a.a
Level 6
Weight 10
Character orbit 6.a
Self dual Yes
Analytic conductor 3.090
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 6.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(3.09021501698\)
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

\(f(q)\) \(=\) \( q - 16q^{2} + 81q^{3} + 256q^{4} + 2694q^{5} - 1296q^{6} - 3544q^{7} - 4096q^{8} + 6561q^{9} + O(q^{10}) \) \( q - 16q^{2} + 81q^{3} + 256q^{4} + 2694q^{5} - 1296q^{6} - 3544q^{7} - 4096q^{8} + 6561q^{9} - 43104q^{10} + 29580q^{11} + 20736q^{12} - 44818q^{13} + 56704q^{14} + 218214q^{15} + 65536q^{16} - 101934q^{17} - 104976q^{18} - 895084q^{19} + 689664q^{20} - 287064q^{21} - 473280q^{22} - 1113000q^{23} - 331776q^{24} + 5304511q^{25} + 717088q^{26} + 531441q^{27} - 907264q^{28} - 2357346q^{29} - 3491424q^{30} + 175808q^{31} - 1048576q^{32} + 2395980q^{33} + 1630944q^{34} - 9547536q^{35} + 1679616q^{36} - 2919418q^{37} + 14321344q^{38} - 3630258q^{39} - 11034624q^{40} + 26218794q^{41} + 4593024q^{42} - 18762964q^{43} + 7572480q^{44} + 17675334q^{45} + 17808000q^{46} - 20966160q^{47} + 5308416q^{48} - 27793671q^{49} - 84872176q^{50} - 8256654q^{51} - 11473408q^{52} + 57251574q^{53} - 8503056q^{54} + 79688520q^{55} + 14516224q^{56} - 72501804q^{57} + 37717536q^{58} + 33587580q^{59} + 55862784q^{60} + 82260830q^{61} - 2812928q^{62} - 23252184q^{63} + 16777216q^{64} - 120739692q^{65} - 38335680q^{66} - 188455804q^{67} - 26095104q^{68} - 90153000q^{69} + 152760576q^{70} + 80924040q^{71} - 26873856q^{72} - 236140918q^{73} + 46710688q^{74} + 429665391q^{75} - 229141504q^{76} - 104831520q^{77} + 58084128q^{78} + 526909808q^{79} + 176553984q^{80} + 43046721q^{81} - 419500704q^{82} + 18346452q^{83} - 73488384q^{84} - 274610196q^{85} + 300207424q^{86} - 190945026q^{87} - 121159680q^{88} + 690643098q^{89} - 282805344q^{90} + 158834992q^{91} - 284928000q^{92} + 14240448q^{93} + 335458560q^{94} - 2411356296q^{95} - 84934656q^{96} - 438251038q^{97} + 444698736q^{98} + 194074380q^{99} + O(q^{100}) \)

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
−16.0000 81.0000 256.000 2694.00 −1296.00 −3544.00 −4096.00 6561.00 −43104.0
\(n\): 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
\(2\) \(1\)
\(3\) \(-1\)

Hecke kernels

There are no other newforms in \(S_{10}^{\mathrm{new}}(\Gamma_0(6))\).