Properties

Label 2646.2.a.p
Level $2646$
Weight $2$
Character orbit 2646.a
Self dual yes
Analytic conductor $21.128$
Analytic rank $0$
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: \(0\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{4} - 4q^{5} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} - 4q^{5} + q^{8} - 4q^{10} - 4q^{11} - 3q^{13} + q^{16} + 7q^{17} - 2q^{19} - 4q^{20} - 4q^{22} - q^{23} + 11q^{25} - 3q^{26} + q^{29} + 9q^{31} + q^{32} + 7q^{34} + 2q^{37} - 2q^{38} - 4q^{40} - 6q^{41} + 11q^{43} - 4q^{44} - q^{46} + 6q^{47} + 11q^{50} - 3q^{52} - 9q^{53} + 16q^{55} + q^{58} + 5q^{59} + 6q^{61} + 9q^{62} + q^{64} + 12q^{65} + 7q^{67} + 7q^{68} - 7q^{71} + 14q^{73} + 2q^{74} - 2q^{76} - 6q^{79} - 4q^{80} - 6q^{82} + 4q^{83} - 28q^{85} + 11q^{86} - 4q^{88} + 3q^{89} - q^{92} + 6q^{94} + 8q^{95} + 8q^{97} + O(q^{100}) \)

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 −4.00000 0 0 1.00000 0 −4.00000
\(n\): 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.p 1
3.b odd 2 1 2646.2.a.o 1
7.b odd 2 1 378.2.a.h yes 1
21.c even 2 1 378.2.a.a 1
28.d even 2 1 3024.2.a.bd 1
35.c odd 2 1 9450.2.a.bc 1
63.l odd 6 2 1134.2.f.a 2
63.o even 6 2 1134.2.f.p 2
84.h odd 2 1 3024.2.a.a 1
105.g even 2 1 9450.2.a.dv 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
378.2.a.a 1 21.c even 2 1
378.2.a.h yes 1 7.b odd 2 1
1134.2.f.a 2 63.l odd 6 2
1134.2.f.p 2 63.o even 6 2
2646.2.a.o 1 3.b odd 2 1
2646.2.a.p 1 1.a even 1 1 trivial
3024.2.a.a 1 84.h odd 2 1
3024.2.a.bd 1 28.d even 2 1
9450.2.a.bc 1 35.c odd 2 1
9450.2.a.dv 1 105.g even 2 1

Hecke kernels

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

\( T_{5} + 4 \)
\( T_{11} + 4 \)
\( T_{13} + 3 \)
\( T_{17} - 7 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( T \)
$5$ \( 4 + T \)
$7$ \( T \)
$11$ \( 4 + T \)
$13$ \( 3 + T \)
$17$ \( -7 + T \)
$19$ \( 2 + T \)
$23$ \( 1 + T \)
$29$ \( -1 + T \)
$31$ \( -9 + T \)
$37$ \( -2 + T \)
$41$ \( 6 + T \)
$43$ \( -11 + T \)
$47$ \( -6 + T \)
$53$ \( 9 + T \)
$59$ \( -5 + T \)
$61$ \( -6 + T \)
$67$ \( -7 + T \)
$71$ \( 7 + T \)
$73$ \( -14 + T \)
$79$ \( 6 + T \)
$83$ \( -4 + T \)
$89$ \( -3 + T \)
$97$ \( -8 + T \)
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