Properties

Label 2541.2.a.l
Level 2541
Weight 2
Character orbit 2541.a
Self dual yes
Analytic conductor 20.290
Analytic rank 1
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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{2} - q^{3} + 2q^{4} + q^{5} - 2q^{6} + q^{7} + q^{9} + O(q^{10}) \) \( q + 2q^{2} - q^{3} + 2q^{4} + q^{5} - 2q^{6} + q^{7} + q^{9} + 2q^{10} - 2q^{12} - 6q^{13} + 2q^{14} - q^{15} - 4q^{16} - 7q^{17} + 2q^{18} - 8q^{19} + 2q^{20} - q^{21} + 6q^{23} - 4q^{25} - 12q^{26} - q^{27} + 2q^{28} + 4q^{29} - 2q^{30} + 2q^{31} - 8q^{32} - 14q^{34} + q^{35} + 2q^{36} - 6q^{37} - 16q^{38} + 6q^{39} - 2q^{41} - 2q^{42} - q^{43} + q^{45} + 12q^{46} + 13q^{47} + 4q^{48} + q^{49} - 8q^{50} + 7q^{51} - 12q^{52} - 2q^{54} + 8q^{57} + 8q^{58} + q^{59} - 2q^{60} - 10q^{61} + 4q^{62} + q^{63} - 8q^{64} - 6q^{65} - 3q^{67} - 14q^{68} - 6q^{69} + 2q^{70} - 6q^{71} + 14q^{73} - 12q^{74} + 4q^{75} - 16q^{76} + 12q^{78} + 4q^{79} - 4q^{80} + q^{81} - 4q^{82} - 5q^{83} - 2q^{84} - 7q^{85} - 2q^{86} - 4q^{87} + 3q^{89} + 2q^{90} - 6q^{91} + 12q^{92} - 2q^{93} + 26q^{94} - 8q^{95} + 8q^{96} - 4q^{97} + 2q^{98} + O(q^{100}) \)

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
2.00000 −1.00000 2.00000 1.00000 −2.00000 1.00000 0 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.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2541.2.a.l yes 1
3.b odd 2 1 7623.2.a.a 1
11.b odd 2 1 2541.2.a.b 1
33.d even 2 1 7623.2.a.q 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2541.2.a.b 1 11.b odd 2 1
2541.2.a.l yes 1 1.a even 1 1 trivial
7623.2.a.a 1 3.b odd 2 1
7623.2.a.q 1 33.d even 2 1

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(7\) \(-1\)
\(11\) \(-1\)

Hecke kernels

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

\( T_{2} - 2 \)
\( T_{5} - 1 \)
\( T_{13} + 6 \)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 - 2 T + 2 T^{2} \)
$3$ \( 1 + T \)
$5$ \( 1 - T + 5 T^{2} \)
$7$ \( 1 - T \)
$11$ \( \)
$13$ \( 1 + 6 T + 13 T^{2} \)
$17$ \( 1 + 7 T + 17 T^{2} \)
$19$ \( 1 + 8 T + 19 T^{2} \)
$23$ \( 1 - 6 T + 23 T^{2} \)
$29$ \( 1 - 4 T + 29 T^{2} \)
$31$ \( 1 - 2 T + 31 T^{2} \)
$37$ \( 1 + 6 T + 37 T^{2} \)
$41$ \( 1 + 2 T + 41 T^{2} \)
$43$ \( 1 + T + 43 T^{2} \)
$47$ \( 1 - 13 T + 47 T^{2} \)
$53$ \( 1 + 53 T^{2} \)
$59$ \( 1 - T + 59 T^{2} \)
$61$ \( 1 + 10 T + 61 T^{2} \)
$67$ \( 1 + 3 T + 67 T^{2} \)
$71$ \( 1 + 6 T + 71 T^{2} \)
$73$ \( 1 - 14 T + 73 T^{2} \)
$79$ \( 1 - 4 T + 79 T^{2} \)
$83$ \( 1 + 5 T + 83 T^{2} \)
$89$ \( 1 - 3 T + 89 T^{2} \)
$97$ \( 1 + 4 T + 97 T^{2} \)
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