Properties

Label 2646.2.a.f
Level $2646$
Weight $2$
Character orbit 2646.a
Self dual yes
Analytic conductor $21.128$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(21.1284163748\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 378)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{8} - 5q^{13} + q^{16} + 3q^{17} - 2q^{19} + 9q^{23} - 5q^{25} + 5q^{26} + 3q^{29} - 5q^{31} - q^{32} - 3q^{34} + 2q^{37} + 2q^{38} - 6q^{41} - q^{43} - 9q^{46} - 6q^{47} + 5q^{50} - 5q^{52} - 3q^{53} - 3q^{58} - 3q^{59} + 10q^{61} + 5q^{62} + q^{64} - 13q^{67} + 3q^{68} - 9q^{71} - 2q^{73} - 2q^{74} - 2q^{76} - 10q^{79} + 6q^{82} - 12q^{83} + q^{86} + 15q^{89} + 9q^{92} + 6q^{94} - 8q^{97} + O(q^{100}) \)

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 0 1.00000 0 0 0 −1.00000 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)
\(7\) \(-1\)

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 2646.2.a.f 1
3.b odd 2 1 2646.2.a.y 1
7.b odd 2 1 378.2.a.d 1
21.c even 2 1 378.2.a.e yes 1
28.d even 2 1 3024.2.a.o 1
35.c odd 2 1 9450.2.a.cl 1
63.l odd 6 2 1134.2.f.k 2
63.o even 6 2 1134.2.f.e 2
84.h odd 2 1 3024.2.a.p 1
105.g even 2 1 9450.2.a.l 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
378.2.a.d 1 7.b odd 2 1
378.2.a.e yes 1 21.c even 2 1
1134.2.f.e 2 63.o even 6 2
1134.2.f.k 2 63.l odd 6 2
2646.2.a.f 1 1.a even 1 1 trivial
2646.2.a.y 1 3.b odd 2 1
3024.2.a.o 1 28.d even 2 1
3024.2.a.p 1 84.h odd 2 1
9450.2.a.l 1 105.g even 2 1
9450.2.a.cl 1 35.c odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2646))\):

\( T_{5} \)
\( T_{11} \)
\( T_{13} + 5 \)
\( T_{17} - 3 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( T \)
$11$ \( T \)
$13$ \( 5 + T \)
$17$ \( -3 + T \)
$19$ \( 2 + T \)
$23$ \( -9 + T \)
$29$ \( -3 + T \)
$31$ \( 5 + T \)
$37$ \( -2 + T \)
$41$ \( 6 + T \)
$43$ \( 1 + T \)
$47$ \( 6 + T \)
$53$ \( 3 + T \)
$59$ \( 3 + T \)
$61$ \( -10 + T \)
$67$ \( 13 + T \)
$71$ \( 9 + T \)
$73$ \( 2 + T \)
$79$ \( 10 + T \)
$83$ \( 12 + T \)
$89$ \( -15 + T \)
$97$ \( 8 + T \)
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