Properties

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

Related objects

Downloads

Learn more about

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: no (minimal twist has level 51)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{4} + 3q^{5} + 4q^{7} + O(q^{10}) \) \( q - 2q^{4} + 3q^{5} + 4q^{7} - 3q^{11} - q^{13} + 4q^{16} - q^{19} - 6q^{20} + 9q^{23} + 4q^{25} - 8q^{28} + 6q^{29} - 2q^{31} + 12q^{35} + 4q^{37} - 3q^{41} - 7q^{43} + 6q^{44} + 6q^{47} + 9q^{49} + 2q^{52} + 6q^{53} - 9q^{55} - 6q^{59} - 8q^{61} - 8q^{64} - 3q^{65} - 4q^{67} + 12q^{71} - 2q^{73} + 2q^{76} - 12q^{77} + 10q^{79} + 12q^{80} + 6q^{83} - 4q^{91} - 18q^{92} - 3q^{95} + 16q^{97} + O(q^{100}) \)

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
0 0 −2.00000 3.00000 0 4.00000 0 0 0
\(n\): 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.f 1
3.b odd 2 1 867.2.a.c 1
17.b even 2 1 153.2.a.b 1
51.c odd 2 1 51.2.a.a 1
51.f odd 4 2 867.2.d.a 2
51.g odd 8 4 867.2.e.e 4
51.i even 16 8 867.2.h.c 8
68.d odd 2 1 2448.2.a.c 1
85.c even 2 1 3825.2.a.i 1
119.d odd 2 1 7497.2.a.j 1
136.e odd 2 1 9792.2.a.cd 1
136.h even 2 1 9792.2.a.by 1
204.h even 2 1 816.2.a.g 1
255.h odd 2 1 1275.2.a.d 1
255.o even 4 2 1275.2.b.b 2
357.c even 2 1 2499.2.a.d 1
408.b odd 2 1 3264.2.a.a 1
408.h even 2 1 3264.2.a.r 1
561.h even 2 1 6171.2.a.e 1
663.g odd 2 1 8619.2.a.g 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
51.2.a.a 1 51.c odd 2 1
153.2.a.b 1 17.b even 2 1
816.2.a.g 1 204.h even 2 1
867.2.a.c 1 3.b odd 2 1
867.2.d.a 2 51.f odd 4 2
867.2.e.e 4 51.g odd 8 4
867.2.h.c 8 51.i even 16 8
1275.2.a.d 1 255.h odd 2 1
1275.2.b.b 2 255.o even 4 2
2448.2.a.c 1 68.d odd 2 1
2499.2.a.d 1 357.c even 2 1
2601.2.a.f 1 1.a even 1 1 trivial
3264.2.a.a 1 408.b odd 2 1
3264.2.a.r 1 408.h even 2 1
3825.2.a.i 1 85.c even 2 1
6171.2.a.e 1 561.h even 2 1
7497.2.a.j 1 119.d odd 2 1
8619.2.a.g 1 663.g odd 2 1
9792.2.a.by 1 136.h even 2 1
9792.2.a.cd 1 136.e odd 2 1

Hecke kernels

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

\( T_{2} \)
\( T_{5} - 3 \)
\( T_{7} - 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( -3 + T \)
$7$ \( -4 + T \)
$11$ \( 3 + T \)
$13$ \( 1 + T \)
$17$ \( T \)
$19$ \( 1 + T \)
$23$ \( -9 + T \)
$29$ \( -6 + T \)
$31$ \( 2 + T \)
$37$ \( -4 + T \)
$41$ \( 3 + T \)
$43$ \( 7 + T \)
$47$ \( -6 + T \)
$53$ \( -6 + T \)
$59$ \( 6 + T \)
$61$ \( 8 + T \)
$67$ \( 4 + T \)
$71$ \( -12 + T \)
$73$ \( 2 + T \)
$79$ \( -10 + T \)
$83$ \( -6 + T \)
$89$ \( T \)
$97$ \( -16 + T \)
show more
show less