Properties

Label 2541.2.a.a
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

\(f(q)\) \(=\) \( q - 2q^{2} - q^{3} + 2q^{4} - 3q^{5} + 2q^{6} + q^{7} + q^{9} + O(q^{10}) \) \( q - 2q^{2} - q^{3} + 2q^{4} - 3q^{5} + 2q^{6} + q^{7} + q^{9} + 6q^{10} - 2q^{12} - 2q^{13} - 2q^{14} + 3q^{15} - 4q^{16} - 3q^{17} - 2q^{18} + 4q^{19} - 6q^{20} - q^{21} + 2q^{23} + 4q^{25} + 4q^{26} - q^{27} + 2q^{28} - 8q^{29} - 6q^{30} + 2q^{31} + 8q^{32} + 6q^{34} - 3q^{35} + 2q^{36} + 10q^{37} - 8q^{38} + 2q^{39} - 2q^{41} + 2q^{42} - 9q^{43} - 3q^{45} - 4q^{46} + 9q^{47} + 4q^{48} + q^{49} - 8q^{50} + 3q^{51} - 4q^{52} - 8q^{53} + 2q^{54} - 4q^{57} + 16q^{58} - 3q^{59} + 6q^{60} + 10q^{61} - 4q^{62} + q^{63} - 8q^{64} + 6q^{65} + 13q^{67} - 6q^{68} - 2q^{69} + 6q^{70} + 14q^{71} + 10q^{73} - 20q^{74} - 4q^{75} + 8q^{76} - 4q^{78} + 4q^{79} + 12q^{80} + q^{81} + 4q^{82} - q^{83} - 2q^{84} + 9q^{85} + 18q^{86} + 8q^{87} - 9q^{89} + 6q^{90} - 2q^{91} + 4q^{92} - 2q^{93} - 18q^{94} - 12q^{95} - 8q^{96} - 16q^{97} - 2q^{98} + O(q^{100}) \)

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 −3.00000 2.00000 1.00000 0 1.00000 6.00000
\(n\): 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.a 1
3.b odd 2 1 7623.2.a.s 1
11.b odd 2 1 2541.2.a.k yes 1
33.d even 2 1 7623.2.a.d 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2541.2.a.a 1 1.a even 1 1 trivial
2541.2.a.k yes 1 11.b odd 2 1
7623.2.a.d 1 33.d even 2 1
7623.2.a.s 1 3.b odd 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2541))\):

\( T_{2} + 2 \)
\( T_{5} + 3 \)
\( T_{13} + 2 \)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T + 2 T^{2} \)
$3$ \( 1 + T \)
$5$ \( 1 + 3 T + 5 T^{2} \)
$7$ \( 1 - T \)
$11$ \( \)
$13$ \( 1 + 2 T + 13 T^{2} \)
$17$ \( 1 + 3 T + 17 T^{2} \)
$19$ \( 1 - 4 T + 19 T^{2} \)
$23$ \( 1 - 2 T + 23 T^{2} \)
$29$ \( 1 + 8 T + 29 T^{2} \)
$31$ \( 1 - 2 T + 31 T^{2} \)
$37$ \( 1 - 10 T + 37 T^{2} \)
$41$ \( 1 + 2 T + 41 T^{2} \)
$43$ \( 1 + 9 T + 43 T^{2} \)
$47$ \( 1 - 9 T + 47 T^{2} \)
$53$ \( 1 + 8 T + 53 T^{2} \)
$59$ \( 1 + 3 T + 59 T^{2} \)
$61$ \( 1 - 10 T + 61 T^{2} \)
$67$ \( 1 - 13 T + 67 T^{2} \)
$71$ \( 1 - 14 T + 71 T^{2} \)
$73$ \( 1 - 10 T + 73 T^{2} \)
$79$ \( 1 - 4 T + 79 T^{2} \)
$83$ \( 1 + T + 83 T^{2} \)
$89$ \( 1 + 9 T + 89 T^{2} \)
$97$ \( 1 + 16 T + 97 T^{2} \)
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