Properties

Label 1088.2.a.n
Level $1088$
Weight $2$
Character orbit 1088.a
Self dual yes
Analytic conductor $8.688$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1088 = 2^{6} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1088.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.68772373992\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 136)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2 q^{3} + 2 q^{5} - 2 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{3} + 2 q^{5} - 2 q^{7} + q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{15} + q^{17} - 4 q^{21} + 6 q^{23} - q^{25} - 4 q^{27} + 10 q^{29} + 2 q^{31} + 12 q^{33} - 4 q^{35} - 6 q^{37} - 4 q^{39} - 6 q^{41} + 8 q^{43} + 2 q^{45} - 3 q^{49} + 2 q^{51} + 10 q^{53} + 12 q^{55} + 8 q^{59} - 14 q^{61} - 2 q^{63} - 4 q^{65} - 4 q^{67} + 12 q^{69} + 2 q^{71} - 14 q^{73} - 2 q^{75} - 12 q^{77} - 10 q^{79} - 11 q^{81} - 8 q^{83} + 2 q^{85} + 20 q^{87} - 10 q^{89} + 4 q^{91} + 4 q^{93} + 2 q^{97} + 6 q^{99}+O(q^{100}) \) 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 2.00000 0 −2.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(17\) \(-1\)

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 1088.2.a.n 1
3.b odd 2 1 9792.2.a.j 1
4.b odd 2 1 1088.2.a.e 1
8.b even 2 1 136.2.a.a 1
8.d odd 2 1 272.2.a.c 1
12.b even 2 1 9792.2.a.m 1
24.f even 2 1 2448.2.a.q 1
24.h odd 2 1 1224.2.a.g 1
40.e odd 2 1 6800.2.a.d 1
40.f even 2 1 3400.2.a.g 1
40.i odd 4 2 3400.2.e.a 2
56.h odd 2 1 6664.2.a.e 1
136.e odd 2 1 4624.2.a.c 1
136.h even 2 1 2312.2.a.d 1
136.i even 4 2 2312.2.b.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
136.2.a.a 1 8.b even 2 1
272.2.a.c 1 8.d odd 2 1
1088.2.a.e 1 4.b odd 2 1
1088.2.a.n 1 1.a even 1 1 trivial
1224.2.a.g 1 24.h odd 2 1
2312.2.a.d 1 136.h even 2 1
2312.2.b.c 2 136.i even 4 2
2448.2.a.q 1 24.f even 2 1
3400.2.a.g 1 40.f even 2 1
3400.2.e.a 2 40.i odd 4 2
4624.2.a.c 1 136.e odd 2 1
6664.2.a.e 1 56.h odd 2 1
6800.2.a.d 1 40.e odd 2 1
9792.2.a.j 1 3.b odd 2 1
9792.2.a.m 1 12.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1088))\):

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