Properties

Label 270.2.a.b
Level 270
Weight 2
Character orbit 270.a
Self dual Yes
Analytic conductor 2.156
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 270.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(2.15596085457\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} + q^{5} + 2q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} + q^{5} + 2q^{7} - q^{8} - q^{10} - 3q^{11} + 5q^{13} - 2q^{14} + q^{16} + 3q^{17} - 4q^{19} + q^{20} + 3q^{22} + 9q^{23} + q^{25} - 5q^{26} + 2q^{28} + 3q^{29} + 5q^{31} - q^{32} - 3q^{34} + 2q^{35} - 10q^{37} + 4q^{38} - q^{40} - q^{43} - 3q^{44} - 9q^{46} - 9q^{47} - 3q^{49} - q^{50} + 5q^{52} + 12q^{53} - 3q^{55} - 2q^{56} - 3q^{58} - 12q^{59} + 2q^{61} - 5q^{62} + q^{64} + 5q^{65} - 4q^{67} + 3q^{68} - 2q^{70} - 12q^{71} - 10q^{73} + 10q^{74} - 4q^{76} - 6q^{77} - 13q^{79} + q^{80} - 6q^{83} + 3q^{85} + q^{86} + 3q^{88} + 12q^{89} + 10q^{91} + 9q^{92} + 9q^{94} - 4q^{95} + 2q^{97} + 3q^{98} + O(q^{100}) \)

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
−1.00000 0 1.00000 1.00000 0 2.00000 −1.00000 0 −1.00000
\(n\): 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
\(2\) \(1\)
\(3\) \(1\)
\(5\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(270))\):

\( T_{11} + 3 \)
\( T_{13} - 5 \)