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

Downloads

Learn more

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

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

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.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

Hecke kernels

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

\( T_{2} - 1 \) Copy content Toggle raw display
\( T_{5} + 3 \) Copy content Toggle raw display
\( T_{13} - 7 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 1 \) 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
$13$ \( T - 7 \) Copy content Toggle raw display
$17$ \( T - 3 \) Copy content Toggle raw display
$19$ \( T + 2 \) Copy content Toggle raw display
$23$ \( T + 4 \) Copy content Toggle raw display
$29$ \( T - 7 \) Copy content Toggle raw display
$31$ \( T + 10 \) Copy content Toggle raw display
$37$ \( T - 1 \) Copy content Toggle raw display
$41$ \( T + 5 \) Copy content Toggle raw display
$43$ \( T - 6 \) Copy content Toggle raw display
$47$ \( T + 6 \) Copy content Toggle raw display
$53$ \( T + 5 \) Copy content Toggle raw display
$59$ \( T + 6 \) Copy content Toggle raw display
$61$ \( T - 10 \) Copy content Toggle raw display
$67$ \( T + 8 \) Copy content Toggle raw display
$71$ \( T + 10 \) Copy content Toggle raw display
$73$ \( T - 10 \) Copy content Toggle raw display
$79$ \( T + 2 \) Copy content Toggle raw display
$83$ \( T + 16 \) Copy content Toggle raw display
$89$ \( T - 3 \) Copy content Toggle raw display
$97$ \( T + 19 \) Copy content Toggle raw display
show more
show less