Properties

Label 6.4.a.a
Level 6
Weight 4
Character orbit 6.a
Self dual Yes
Analytic conductor 0.354
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 6.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.354011460034\)
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

\(f(q)\) \(=\) \( q - 2q^{2} - 3q^{3} + 4q^{4} + 6q^{5} + 6q^{6} - 16q^{7} - 8q^{8} + 9q^{9} + O(q^{10}) \) \( q - 2q^{2} - 3q^{3} + 4q^{4} + 6q^{5} + 6q^{6} - 16q^{7} - 8q^{8} + 9q^{9} - 12q^{10} + 12q^{11} - 12q^{12} + 38q^{13} + 32q^{14} - 18q^{15} + 16q^{16} - 126q^{17} - 18q^{18} + 20q^{19} + 24q^{20} + 48q^{21} - 24q^{22} + 168q^{23} + 24q^{24} - 89q^{25} - 76q^{26} - 27q^{27} - 64q^{28} + 30q^{29} + 36q^{30} - 88q^{31} - 32q^{32} - 36q^{33} + 252q^{34} - 96q^{35} + 36q^{36} + 254q^{37} - 40q^{38} - 114q^{39} - 48q^{40} + 42q^{41} - 96q^{42} - 52q^{43} + 48q^{44} + 54q^{45} - 336q^{46} - 96q^{47} - 48q^{48} - 87q^{49} + 178q^{50} + 378q^{51} + 152q^{52} + 198q^{53} + 54q^{54} + 72q^{55} + 128q^{56} - 60q^{57} - 60q^{58} - 660q^{59} - 72q^{60} - 538q^{61} + 176q^{62} - 144q^{63} + 64q^{64} + 228q^{65} + 72q^{66} + 884q^{67} - 504q^{68} - 504q^{69} + 192q^{70} + 792q^{71} - 72q^{72} + 218q^{73} - 508q^{74} + 267q^{75} + 80q^{76} - 192q^{77} + 228q^{78} - 520q^{79} + 96q^{80} + 81q^{81} - 84q^{82} - 492q^{83} + 192q^{84} - 756q^{85} + 104q^{86} - 90q^{87} - 96q^{88} + 810q^{89} - 108q^{90} - 608q^{91} + 672q^{92} + 264q^{93} + 192q^{94} + 120q^{95} + 96q^{96} + 1154q^{97} + 174q^{98} + 108q^{99} + O(q^{100}) \)

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 −3.00000 4.00000 6.00000 6.00000 −16.0000 −8.00000 9.00000 −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
\(2\) \(1\)
\(3\) \(1\)

Hecke kernels

There are no other newforms in \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\).