Properties

Label 2601.2.a.a
Level $2601$
Weight $2$
Character orbit 2601.a
Self dual yes
Analytic conductor $20.769$
Analytic rank $2$
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: \(2\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 51)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{2} + 2q^{4} - 3q^{5} - 2q^{7} + O(q^{10}) \) \( q - 2q^{2} + 2q^{4} - 3q^{5} - 2q^{7} + 6q^{10} - 5q^{11} - q^{13} + 4q^{14} - 4q^{16} - 5q^{19} - 6q^{20} + 10q^{22} - q^{23} + 4q^{25} + 2q^{26} - 4q^{28} - 6q^{29} - 10q^{31} + 8q^{32} + 6q^{35} + 2q^{37} + 10q^{38} - 5q^{41} + q^{43} - 10q^{44} + 2q^{46} + 2q^{47} - 3q^{49} - 8q^{50} - 2q^{52} - 6q^{53} + 15q^{55} + 12q^{58} - 10q^{61} + 20q^{62} - 8q^{64} + 3q^{65} - 12q^{67} - 12q^{70} - 6q^{73} - 4q^{74} - 10q^{76} + 10q^{77} + 4q^{79} + 12q^{80} + 10q^{82} - 6q^{83} - 2q^{86} + 10q^{89} + 2q^{91} - 2q^{92} - 4q^{94} + 15q^{95} - 8q^{97} + 6q^{98} + O(q^{100}) \)

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
−2.00000 0 2.00000 −3.00000 0 −2.00000 0 0 6.00000
\(n\): 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.a 1
3.b odd 2 1 867.2.a.e 1
17.b even 2 1 2601.2.a.c 1
17.c even 4 2 153.2.d.c 2
51.c odd 2 1 867.2.a.d 1
51.f odd 4 2 51.2.d.a 2
51.g odd 8 4 867.2.e.a 4
51.i even 16 8 867.2.h.e 8
68.f odd 4 2 2448.2.c.f 2
204.l even 4 2 816.2.c.b 2
255.i odd 4 2 1275.2.g.b 2
255.k even 4 2 1275.2.d.a 2
255.r even 4 2 1275.2.d.c 2
408.q even 4 2 3264.2.c.h 2
408.t odd 4 2 3264.2.c.g 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
51.2.d.a 2 51.f odd 4 2
153.2.d.c 2 17.c even 4 2
816.2.c.b 2 204.l even 4 2
867.2.a.d 1 51.c odd 2 1
867.2.a.e 1 3.b odd 2 1
867.2.e.a 4 51.g odd 8 4
867.2.h.e 8 51.i even 16 8
1275.2.d.a 2 255.k even 4 2
1275.2.d.c 2 255.r even 4 2
1275.2.g.b 2 255.i odd 4 2
2448.2.c.f 2 68.f odd 4 2
2601.2.a.a 1 1.a even 1 1 trivial
2601.2.a.c 1 17.b even 2 1
3264.2.c.g 2 408.t odd 4 2
3264.2.c.h 2 408.q even 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2601))\):

\( T_{2} + 2 \)
\( T_{5} + 3 \)
\( T_{7} + 2 \)

Hecke characteristic polynomials

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