Properties

Label 2888.2.a.c
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

\(f(q)\) \(=\) \( q - q^{3} + 3 q^{5} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{3} + 3 q^{5} - 2 q^{9} - 4 q^{11} + 5 q^{13} - 3 q^{15} - 5 q^{17} - q^{23} + 4 q^{25} + 5 q^{27} - 3 q^{29} - 4 q^{31} + 4 q^{33} - 2 q^{37} - 5 q^{39} + 5 q^{41} - 11 q^{43} - 6 q^{45} - 5 q^{47} - 7 q^{49} + 5 q^{51} + 9 q^{53} - 12 q^{55} - 13 q^{59} - q^{61} + 15 q^{65} + 5 q^{67} + q^{69} - q^{71} - 9 q^{73} - 4 q^{75} - 17 q^{79} + q^{81} + 16 q^{83} - 15 q^{85} + 3 q^{87} - 3 q^{89} + 4 q^{93} + 13 q^{97} + 8 q^{99}+O(q^{100}) \) 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 −1.00000 0 3.00000 0 0 0 −2.00000 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.c 1
4.b odd 2 1 5776.2.a.o 1
19.b odd 2 1 2888.2.a.e 1
19.d odd 6 2 152.2.i.a 2
57.f even 6 2 1368.2.s.g 2
76.d even 2 1 5776.2.a.h 1
76.f even 6 2 304.2.i.b 2
152.l odd 6 2 1216.2.i.i 2
152.o even 6 2 1216.2.i.e 2
228.n odd 6 2 2736.2.s.q 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
152.2.i.a 2 19.d odd 6 2
304.2.i.b 2 76.f even 6 2
1216.2.i.e 2 152.o even 6 2
1216.2.i.i 2 152.l odd 6 2
1368.2.s.g 2 57.f even 6 2
2736.2.s.q 2 228.n odd 6 2
2888.2.a.c 1 1.a even 1 1 trivial
2888.2.a.e 1 19.b odd 2 1
5776.2.a.h 1 76.d even 2 1
5776.2.a.o 1 4.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2888))\):

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

Hecke characteristic polynomials

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