Properties

Label 2541.2.a.j
Level 2541
Weight 2
Character orbit 2541.a
Self dual Yes
Analytic conductor 20.290
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2541.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(20.2899871536\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} - q^{4} - 2q^{5} + q^{6} + q^{7} - 3q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} - q^{4} - 2q^{5} + q^{6} + q^{7} - 3q^{8} + q^{9} - 2q^{10} - q^{12} + 2q^{13} + q^{14} - 2q^{15} - q^{16} + 6q^{17} + q^{18} - 4q^{19} + 2q^{20} + q^{21} - 3q^{24} - q^{25} + 2q^{26} + q^{27} - q^{28} + 2q^{29} - 2q^{30} + 5q^{32} + 6q^{34} - 2q^{35} - q^{36} + 6q^{37} - 4q^{38} + 2q^{39} + 6q^{40} - 2q^{41} + q^{42} + 4q^{43} - 2q^{45} - q^{48} + q^{49} - q^{50} + 6q^{51} - 2q^{52} + 6q^{53} + q^{54} - 3q^{56} - 4q^{57} + 2q^{58} + 12q^{59} + 2q^{60} + 2q^{61} + q^{63} + 7q^{64} - 4q^{65} + 4q^{67} - 6q^{68} - 2q^{70} - 3q^{72} + 6q^{73} + 6q^{74} - q^{75} + 4q^{76} + 2q^{78} + 16q^{79} + 2q^{80} + q^{81} - 2q^{82} + 12q^{83} - q^{84} - 12q^{85} + 4q^{86} + 2q^{87} - 14q^{89} - 2q^{90} + 2q^{91} + 8q^{95} + 5q^{96} + 18q^{97} + q^{98} + O(q^{100}) \)

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 1.00000 −1.00000 −2.00000 1.00000 1.00000 −3.00000 1.00000 −2.00000
\(n\): 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
\(3\) \(-1\)
\(7\) \(-1\)
\(11\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2541))\):

\( T_{2} - 1 \)
\( T_{5} + 2 \)
\( T_{13} - 2 \)