Properties

Label 16.26.a.b
Level $16$
Weight $26$
Character orbit 16.a
Self dual yes
Analytic conductor $63.359$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 16.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.3594847924\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 195804 q^{3} - 741989850 q^{5} - 39080597192 q^{7} - 808949403027 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 195804 q^{3} - 741989850 q^{5} - 39080597192 q^{7} - 808949403027 q^{9} - 8419515299052 q^{11} - 81651045335314 q^{13} - 145284580589400 q^{15} - 25\!\cdots\!78 q^{17}+ \cdots + 68\!\cdots\!04 q^{99}+O(q^{100}) \) 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 195804. 0 −7.41990e8 0 −3.90806e10 0 −8.08949e11 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 16.26.a.b 1
4.b odd 2 1 1.26.a.a 1
12.b even 2 1 9.26.a.a 1
20.d odd 2 1 25.26.a.a 1
20.e even 4 2 25.26.b.a 2
28.d even 2 1 49.26.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1.26.a.a 1 4.b odd 2 1
9.26.a.a 1 12.b even 2 1
16.26.a.b 1 1.a even 1 1 trivial
25.26.a.a 1 20.d odd 2 1
25.26.b.a 2 20.e even 4 2
49.26.a.a 1 28.d even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 195804 \) acting on \(S_{26}^{\mathrm{new}}(\Gamma_0(16))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T - 195804 \) Copy content Toggle raw display
$5$ \( T + 741989850 \) Copy content Toggle raw display
$7$ \( T + 39080597192 \) Copy content Toggle raw display
$11$ \( T + 8419515299052 \) Copy content Toggle raw display
$13$ \( T + 81651045335314 \) Copy content Toggle raw display
$17$ \( T + 2519900028948078 \) Copy content Toggle raw display
$19$ \( T - 6082056370308940 \) Copy content Toggle raw display
$23$ \( T - 94\!\cdots\!24 \) Copy content Toggle raw display
$29$ \( T + 27\!\cdots\!10 \) Copy content Toggle raw display
$31$ \( T + 42\!\cdots\!52 \) Copy content Toggle raw display
$37$ \( T - 20\!\cdots\!82 \) Copy content Toggle raw display
$41$ \( T + 18\!\cdots\!98 \) Copy content Toggle raw display
$43$ \( T + 30\!\cdots\!56 \) Copy content Toggle raw display
$47$ \( T - 92\!\cdots\!88 \) Copy content Toggle raw display
$53$ \( T + 99\!\cdots\!54 \) Copy content Toggle raw display
$59$ \( T + 13\!\cdots\!80 \) Copy content Toggle raw display
$61$ \( T - 90\!\cdots\!02 \) Copy content Toggle raw display
$67$ \( T - 26\!\cdots\!28 \) Copy content Toggle raw display
$71$ \( T - 19\!\cdots\!48 \) Copy content Toggle raw display
$73$ \( T - 42\!\cdots\!26 \) Copy content Toggle raw display
$79$ \( T - 27\!\cdots\!60 \) Copy content Toggle raw display
$83$ \( T - 93\!\cdots\!84 \) Copy content Toggle raw display
$89$ \( T + 17\!\cdots\!30 \) Copy content Toggle raw display
$97$ \( T - 28\!\cdots\!62 \) Copy content Toggle raw display
show more
show less