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 $1$

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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

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

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:

Atkin-Lehner signs

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

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

Hecke kernels

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

\( T_{2} + 2 \) Copy content Toggle raw display
\( T_{5} + 3 \) Copy content Toggle raw display
\( T_{13} + 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

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