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

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

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
−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 \(T_{2} \) \(\mathstrut +\mathstrut 3 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(27))\).