Properties

Label 27.4.a.a
Level 27
Weight 4
Character orbit 27.a
Self dual Yes
Analytic conductor 1.593
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 27.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.59305157016\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q - 3q^{2} + q^{4} - 15q^{5} - 25q^{7} + 21q^{8} + O(q^{10}) \) \( q - 3q^{2} + q^{4} - 15q^{5} - 25q^{7} + 21q^{8} + 45q^{10} + 15q^{11} + 20q^{13} + 75q^{14} - 71q^{16} - 72q^{17} + 2q^{19} - 15q^{20} - 45q^{22} - 114q^{23} + 100q^{25} - 60q^{26} - 25q^{28} - 30q^{29} + 101q^{31} + 45q^{32} + 216q^{34} + 375q^{35} - 430q^{37} - 6q^{38} - 315q^{40} + 30q^{41} + 110q^{43} + 15q^{44} + 342q^{46} + 330q^{47} + 282q^{49} - 300q^{50} + 20q^{52} - 621q^{53} - 225q^{55} - 525q^{56} + 90q^{58} + 660q^{59} - 376q^{61} - 303q^{62} + 433q^{64} - 300q^{65} - 250q^{67} - 72q^{68} - 1125q^{70} + 360q^{71} + 785q^{73} + 1290q^{74} + 2q^{76} - 375q^{77} + 488q^{79} + 1065q^{80} - 90q^{82} - 489q^{83} + 1080q^{85} - 330q^{86} + 315q^{88} + 450q^{89} - 500q^{91} - 114q^{92} - 990q^{94} - 30q^{95} - 1105q^{97} - 846q^{98} + O(q^{100}) \)

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
−3.00000 0 1.00000 −15.0000 0 −25.0000 21.0000 0 45.0000
\(n\): 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
\(3\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} + 3 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(27))\).