Properties

Label 108.4.a.c
Level $108$
Weight $4$
Character orbit 108.a
Self dual yes
Analytic conductor $6.372$
Analytic rank $0$
Dimension $1$
CM discriminant -3
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $N(\mathrm{U}(1))$

$q$-expansion

\(f(q)\) \(=\) \( q + 17q^{7} + O(q^{10}) \) \( q + 17q^{7} + 89q^{13} + 107q^{19} - 125q^{25} + 308q^{31} - 433q^{37} - 520q^{43} - 54q^{49} - 901q^{61} + 1007q^{67} - 271q^{73} + 503q^{79} + 1513q^{91} + 1853q^{97} + O(q^{100}) \)

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 0 0 0 17.0000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 CM by \(\Q(\sqrt{-3}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 108.4.a.c 1
3.b odd 2 1 CM 108.4.a.c 1
4.b odd 2 1 432.4.a.g 1
8.b even 2 1 1728.4.a.q 1
8.d odd 2 1 1728.4.a.p 1
9.c even 3 2 324.4.e.d 2
9.d odd 6 2 324.4.e.d 2
12.b even 2 1 432.4.a.g 1
24.f even 2 1 1728.4.a.p 1
24.h odd 2 1 1728.4.a.q 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
108.4.a.c 1 1.a even 1 1 trivial
108.4.a.c 1 3.b odd 2 1 CM
324.4.e.d 2 9.c even 3 2
324.4.e.d 2 9.d odd 6 2
432.4.a.g 1 4.b odd 2 1
432.4.a.g 1 12.b even 2 1
1728.4.a.p 1 8.d odd 2 1
1728.4.a.p 1 24.f even 2 1
1728.4.a.q 1 8.b even 2 1
1728.4.a.q 1 24.h odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(108))\):

\( T_{5} \)
\( T_{7} - 17 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( -17 + T \)
$11$ \( T \)
$13$ \( -89 + T \)
$17$ \( T \)
$19$ \( -107 + T \)
$23$ \( T \)
$29$ \( T \)
$31$ \( -308 + T \)
$37$ \( 433 + T \)
$41$ \( T \)
$43$ \( 520 + T \)
$47$ \( T \)
$53$ \( T \)
$59$ \( T \)
$61$ \( 901 + T \)
$67$ \( -1007 + T \)
$71$ \( T \)
$73$ \( 271 + T \)
$79$ \( -503 + T \)
$83$ \( T \)
$89$ \( T \)
$97$ \( -1853 + T \)
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