Properties

Label 2601.2.a.d
Level $2601$
Weight $2$
Character orbit 2601.a
Self dual yes
Analytic conductor $20.769$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2601 = 3^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2601.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(20.7690895657\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q - q^{2} - q^{4} - 2q^{5} + q^{7} + 3q^{8} + O(q^{10}) \) \( q - q^{2} - q^{4} - 2q^{5} + q^{7} + 3q^{8} + 2q^{10} + 6q^{11} + q^{13} - q^{14} - q^{16} + 5q^{19} + 2q^{20} - 6q^{22} - 2q^{23} - q^{25} - q^{26} - q^{28} - 6q^{29} + 7q^{31} - 5q^{32} - 2q^{35} + 7q^{37} - 5q^{38} - 6q^{40} - 6q^{41} + 7q^{43} - 6q^{44} + 2q^{46} - 12q^{47} - 6q^{49} + q^{50} - q^{52} + 12q^{53} - 12q^{55} + 3q^{56} + 6q^{58} - 6q^{59} + 11q^{61} - 7q^{62} + 7q^{64} - 2q^{65} - 11q^{67} + 2q^{70} + 2q^{71} - 6q^{73} - 7q^{74} - 5q^{76} + 6q^{77} + 2q^{80} + 6q^{82} + 2q^{83} - 7q^{86} + 18q^{88} + 16q^{89} + q^{91} + 2q^{92} + 12q^{94} - 10q^{95} + 17q^{97} + 6q^{98} + O(q^{100}) \)

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 −2.00000 0 1.00000 3.00000 0 2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 2601.2.a.d 1
3.b odd 2 1 2601.2.a.k yes 1
17.b even 2 1 2601.2.a.e yes 1
51.c odd 2 1 2601.2.a.h yes 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2601.2.a.d 1 1.a even 1 1 trivial
2601.2.a.e yes 1 17.b even 2 1
2601.2.a.h yes 1 51.c odd 2 1
2601.2.a.k yes 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2601))\):

\( T_{2} + 1 \)
\( T_{5} + 2 \)
\( T_{7} - 1 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( T \)
$5$ \( 2 + T \)
$7$ \( -1 + T \)
$11$ \( -6 + T \)
$13$ \( -1 + T \)
$17$ \( T \)
$19$ \( -5 + T \)
$23$ \( 2 + T \)
$29$ \( 6 + T \)
$31$ \( -7 + T \)
$37$ \( -7 + T \)
$41$ \( 6 + T \)
$43$ \( -7 + T \)
$47$ \( 12 + T \)
$53$ \( -12 + T \)
$59$ \( 6 + T \)
$61$ \( -11 + T \)
$67$ \( 11 + T \)
$71$ \( -2 + T \)
$73$ \( 6 + T \)
$79$ \( T \)
$83$ \( -2 + T \)
$89$ \( -16 + T \)
$97$ \( -17 + T \)
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