Properties

Label 2888.2.a.f
Level $2888$
Weight $2$
Character orbit 2888.a
Self dual yes
Analytic conductor $23.061$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2888 = 2^{3} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2888.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(23.0607961037\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 152)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2 q^{3} - q^{5} - 3 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{3} - q^{5} - 3 q^{7} + q^{9} - 3 q^{11} + 4 q^{13} - 2 q^{15} + 5 q^{17} - 6 q^{21} - 4 q^{25} - 4 q^{27} - 2 q^{29} - 8 q^{31} - 6 q^{33} + 3 q^{35} + 10 q^{37} + 8 q^{39} - 6 q^{41} - 7 q^{43} - q^{45} - 9 q^{47} + 2 q^{49} + 10 q^{51} + 8 q^{53} + 3 q^{55} - 14 q^{59} - 5 q^{61} - 3 q^{63} - 4 q^{65} + 6 q^{71} - 15 q^{73} - 8 q^{75} + 9 q^{77} + 4 q^{79} - 11 q^{81} + 4 q^{83} - 5 q^{85} - 4 q^{87} - 12 q^{91} - 16 q^{93} - 16 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(19\) \(-1\)

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 2888.2.a.f 1
4.b odd 2 1 5776.2.a.b 1
19.b odd 2 1 152.2.a.a 1
57.d even 2 1 1368.2.a.h 1
76.d even 2 1 304.2.a.e 1
95.d odd 2 1 3800.2.a.i 1
95.g even 4 2 3800.2.d.d 2
133.c even 2 1 7448.2.a.s 1
152.b even 2 1 1216.2.a.d 1
152.g odd 2 1 1216.2.a.p 1
228.b odd 2 1 2736.2.a.p 1
380.d even 2 1 7600.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
152.2.a.a 1 19.b odd 2 1
304.2.a.e 1 76.d even 2 1
1216.2.a.d 1 152.b even 2 1
1216.2.a.p 1 152.g odd 2 1
1368.2.a.h 1 57.d even 2 1
2736.2.a.p 1 228.b odd 2 1
2888.2.a.f 1 1.a even 1 1 trivial
3800.2.a.i 1 95.d odd 2 1
3800.2.d.d 2 95.g even 4 2
5776.2.a.b 1 4.b odd 2 1
7448.2.a.s 1 133.c even 2 1
7600.2.a.b 1 380.d even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2888))\):

\( T_{3} - 2 \) Copy content Toggle raw display
\( T_{5} + 1 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T - 2 \) Copy content Toggle raw display
$5$ \( T + 1 \) Copy content Toggle raw display
$7$ \( T + 3 \) Copy content Toggle raw display
$11$ \( T + 3 \) Copy content Toggle raw display
$13$ \( T - 4 \) Copy content Toggle raw display
$17$ \( T - 5 \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T \) Copy content Toggle raw display
$29$ \( T + 2 \) Copy content Toggle raw display
$31$ \( T + 8 \) Copy content Toggle raw display
$37$ \( T - 10 \) Copy content Toggle raw display
$41$ \( T + 6 \) Copy content Toggle raw display
$43$ \( T + 7 \) Copy content Toggle raw display
$47$ \( T + 9 \) Copy content Toggle raw display
$53$ \( T - 8 \) Copy content Toggle raw display
$59$ \( T + 14 \) Copy content Toggle raw display
$61$ \( T + 5 \) Copy content Toggle raw display
$67$ \( T \) Copy content Toggle raw display
$71$ \( T - 6 \) Copy content Toggle raw display
$73$ \( T + 15 \) Copy content Toggle raw display
$79$ \( T - 4 \) Copy content Toggle raw display
$83$ \( T - 4 \) Copy content Toggle raw display
$89$ \( T \) Copy content Toggle raw display
$97$ \( T + 16 \) Copy content Toggle raw display
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