Properties

Label 4641.2.a.c
Level $4641$
Weight $2$
Character orbit 4641.a
Self dual yes
Analytic conductor $37.059$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4641 = 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4641.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.0585715781\)
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

\(f(q)\) \(=\) \( q - q^{2} - q^{3} - q^{4} + 2q^{5} + q^{6} - q^{7} + 3q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - q^{3} - q^{4} + 2q^{5} + q^{6} - q^{7} + 3q^{8} + q^{9} - 2q^{10} + 4q^{11} + q^{12} + q^{13} + q^{14} - 2q^{15} - q^{16} + q^{17} - q^{18} + 4q^{19} - 2q^{20} + q^{21} - 4q^{22} - 8q^{23} - 3q^{24} - q^{25} - q^{26} - q^{27} + q^{28} - 6q^{29} + 2q^{30} - 8q^{31} - 5q^{32} - 4q^{33} - q^{34} - 2q^{35} - q^{36} + 2q^{37} - 4q^{38} - q^{39} + 6q^{40} + 6q^{41} - q^{42} - 4q^{43} - 4q^{44} + 2q^{45} + 8q^{46} - 12q^{47} + q^{48} + q^{49} + q^{50} - q^{51} - q^{52} + 6q^{53} + q^{54} + 8q^{55} - 3q^{56} - 4q^{57} + 6q^{58} + 2q^{60} - 14q^{61} + 8q^{62} - q^{63} + 7q^{64} + 2q^{65} + 4q^{66} + 8q^{67} - q^{68} + 8q^{69} + 2q^{70} - 8q^{71} + 3q^{72} + 2q^{73} - 2q^{74} + q^{75} - 4q^{76} - 4q^{77} + q^{78} + 8q^{79} - 2q^{80} + q^{81} - 6q^{82} - q^{84} + 2q^{85} + 4q^{86} + 6q^{87} + 12q^{88} - 14q^{89} - 2q^{90} - q^{91} + 8q^{92} + 8q^{93} + 12q^{94} + 8q^{95} + 5q^{96} + 10q^{97} - q^{98} + 4q^{99} + O(q^{100}) \)

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 2.00000 1.00000 −1.00000 3.00000 1.00000 −2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(7\) \(1\)
\(13\) \(-1\)
\(17\) \(-1\)

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 4641.2.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4641.2.a.c 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4641))\):

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( 1 + T \)
$5$ \( -2 + T \)
$7$ \( 1 + T \)
$11$ \( -4 + T \)
$13$ \( -1 + T \)
$17$ \( -1 + T \)
$19$ \( -4 + T \)
$23$ \( 8 + T \)
$29$ \( 6 + T \)
$31$ \( 8 + T \)
$37$ \( -2 + T \)
$41$ \( -6 + T \)
$43$ \( 4 + T \)
$47$ \( 12 + T \)
$53$ \( -6 + T \)
$59$ \( T \)
$61$ \( 14 + T \)
$67$ \( -8 + T \)
$71$ \( 8 + T \)
$73$ \( -2 + T \)
$79$ \( -8 + T \)
$83$ \( T \)
$89$ \( 14 + T \)
$97$ \( -10 + T \)
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