Properties

Label 2535.2.a.j
Level 2535
Weight 2
Character orbit 2535.a
Self dual Yes
Analytic conductor 20.242
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 2535 = 3 \cdot 5 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2535.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(20.2420769124\)
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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} - 3q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} - 3q^{8} + q^{9} - q^{10} + 4q^{11} + q^{12} + q^{15} - q^{16} + 2q^{17} + q^{18} - 4q^{19} + q^{20} + 4q^{22} + 3q^{24} + q^{25} - q^{27} - 2q^{29} + q^{30} + 5q^{32} - 4q^{33} + 2q^{34} - q^{36} + 10q^{37} - 4q^{38} + 3q^{40} - 10q^{41} + 4q^{43} - 4q^{44} - q^{45} - 8q^{47} + q^{48} - 7q^{49} + q^{50} - 2q^{51} - 10q^{53} - q^{54} - 4q^{55} + 4q^{57} - 2q^{58} + 4q^{59} - q^{60} - 2q^{61} + 7q^{64} - 4q^{66} - 12q^{67} - 2q^{68} + 8q^{71} - 3q^{72} - 10q^{73} + 10q^{74} - q^{75} + 4q^{76} + q^{80} + q^{81} - 10q^{82} - 12q^{83} - 2q^{85} + 4q^{86} + 2q^{87} - 12q^{88} + 6q^{89} - q^{90} - 8q^{94} + 4q^{95} - 5q^{96} - 2q^{97} - 7q^{98} + 4q^{99} + O(q^{100}) \)

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 −1.00000 −1.00000 −1.00000 −1.00000 0 −3.00000 1.00000 −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
\(3\) \(1\)
\(5\) \(1\)
\(13\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2535))\):

\( T_{2} - 1 \)
\( T_{7} \)
\( T_{11} - 4 \)