Properties

Label 18.4.a.a
Level 18
Weight 4
Character orbit 18.a
Self dual Yes
Analytic conductor 1.062
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 18.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.0620343801\)
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

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

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 0 4.00000 −6.00000 0 −16.0000 8.00000 0 −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 \(S_{4}^{\mathrm{new}}(\Gamma_0(18))\).