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

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

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 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(18))\).