Properties

Label 2541.2.a.g
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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} - q^{4} - 3q^{5} - q^{6} + q^{7} - 3q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} - q^{4} - 3q^{5} - q^{6} + q^{7} - 3q^{8} + q^{9} - 3q^{10} + q^{12} + 7q^{13} + q^{14} + 3q^{15} - q^{16} + 3q^{17} + q^{18} - 2q^{19} + 3q^{20} - q^{21} - 4q^{23} + 3q^{24} + 4q^{25} + 7q^{26} - q^{27} - q^{28} + 7q^{29} + 3q^{30} - 10q^{31} + 5q^{32} + 3q^{34} - 3q^{35} - q^{36} + q^{37} - 2q^{38} - 7q^{39} + 9q^{40} - 5q^{41} - q^{42} + 6q^{43} - 3q^{45} - 4q^{46} - 6q^{47} + q^{48} + q^{49} + 4q^{50} - 3q^{51} - 7q^{52} - 5q^{53} - q^{54} - 3q^{56} + 2q^{57} + 7q^{58} - 6q^{59} - 3q^{60} + 10q^{61} - 10q^{62} + q^{63} + 7q^{64} - 21q^{65} - 8q^{67} - 3q^{68} + 4q^{69} - 3q^{70} - 10q^{71} - 3q^{72} + 10q^{73} + q^{74} - 4q^{75} + 2q^{76} - 7q^{78} - 2q^{79} + 3q^{80} + q^{81} - 5q^{82} - 16q^{83} + q^{84} - 9q^{85} + 6q^{86} - 7q^{87} + 3q^{89} - 3q^{90} + 7q^{91} + 4q^{92} + 10q^{93} - 6q^{94} + 6q^{95} - 5q^{96} - 19q^{97} + q^{98} + O(q^{100}) \)

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

\( T_{2} - 1 \)
\( T_{5} + 3 \)
\( T_{13} - 7 \)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 - T + 2 T^{2} \)
$3$ \( 1 + T \)
$5$ \( 1 + 3 T + 5 T^{2} \)
$7$ \( 1 - T \)
$11$ \( \)
$13$ \( 1 - 7 T + 13 T^{2} \)
$17$ \( 1 - 3 T + 17 T^{2} \)
$19$ \( 1 + 2 T + 19 T^{2} \)
$23$ \( 1 + 4 T + 23 T^{2} \)
$29$ \( 1 - 7 T + 29 T^{2} \)
$31$ \( 1 + 10 T + 31 T^{2} \)
$37$ \( 1 - T + 37 T^{2} \)
$41$ \( 1 + 5 T + 41 T^{2} \)
$43$ \( 1 - 6 T + 43 T^{2} \)
$47$ \( 1 + 6 T + 47 T^{2} \)
$53$ \( 1 + 5 T + 53 T^{2} \)
$59$ \( 1 + 6 T + 59 T^{2} \)
$61$ \( 1 - 10 T + 61 T^{2} \)
$67$ \( 1 + 8 T + 67 T^{2} \)
$71$ \( 1 + 10 T + 71 T^{2} \)
$73$ \( 1 - 10 T + 73 T^{2} \)
$79$ \( 1 + 2 T + 79 T^{2} \)
$83$ \( 1 + 16 T + 83 T^{2} \)
$89$ \( 1 - 3 T + 89 T^{2} \)
$97$ \( 1 + 19 T + 97 T^{2} \)
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