Properties

Label 660.2.a.c
Level $660$
Weight $2$
Character orbit 660.a
Self dual yes
Analytic conductor $5.270$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 660.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.27012653340\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} - q^{5} - 4 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{3} - q^{5} - 4 q^{7} + q^{9} - q^{11} - 4 q^{13} - q^{15} - 6 q^{17} + 2 q^{19} - 4 q^{21} + q^{25} + q^{27} - 4 q^{31} - q^{33} + 4 q^{35} - 10 q^{37} - 4 q^{39} - 4 q^{43} - q^{45} + 12 q^{47} + 9 q^{49} - 6 q^{51} + 6 q^{53} + q^{55} + 2 q^{57} + 12 q^{59} - 10 q^{61} - 4 q^{63} + 4 q^{65} - 4 q^{67} + 8 q^{73} + q^{75} + 4 q^{77} - 10 q^{79} + q^{81} - 6 q^{83} + 6 q^{85} - 6 q^{89} + 16 q^{91} - 4 q^{93} - 2 q^{95} - 10 q^{97} - q^{99}+O(q^{100}) \) 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 −1.00000 0 −4.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(1\)
\(11\) \(1\)

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 660.2.a.c 1
3.b odd 2 1 1980.2.a.c 1
4.b odd 2 1 2640.2.a.f 1
5.b even 2 1 3300.2.a.h 1
5.c odd 4 2 3300.2.c.b 2
11.b odd 2 1 7260.2.a.p 1
12.b even 2 1 7920.2.a.bl 1
15.d odd 2 1 9900.2.a.bc 1
15.e even 4 2 9900.2.c.j 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
660.2.a.c 1 1.a even 1 1 trivial
1980.2.a.c 1 3.b odd 2 1
2640.2.a.f 1 4.b odd 2 1
3300.2.a.h 1 5.b even 2 1
3300.2.c.b 2 5.c odd 4 2
7260.2.a.p 1 11.b odd 2 1
7920.2.a.bl 1 12.b even 2 1
9900.2.a.bc 1 15.d odd 2 1
9900.2.c.j 2 15.e even 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(660))\):

\( T_{7} + 4 \) Copy content Toggle raw display
\( T_{13} + 4 \) 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
$5$ \( T + 1 \) Copy content Toggle raw display
$7$ \( T + 4 \) Copy content Toggle raw display
$11$ \( T + 1 \) Copy content Toggle raw display
$13$ \( T + 4 \) Copy content Toggle raw display
$17$ \( T + 6 \) Copy content Toggle raw display
$19$ \( T - 2 \) Copy content Toggle raw display
$23$ \( T \) Copy content Toggle raw display
$29$ \( T \) Copy content Toggle raw display
$31$ \( T + 4 \) Copy content Toggle raw display
$37$ \( T + 10 \) Copy content Toggle raw display
$41$ \( T \) Copy content Toggle raw display
$43$ \( T + 4 \) Copy content Toggle raw display
$47$ \( T - 12 \) Copy content Toggle raw display
$53$ \( T - 6 \) Copy content Toggle raw display
$59$ \( T - 12 \) Copy content Toggle raw display
$61$ \( T + 10 \) Copy content Toggle raw display
$67$ \( T + 4 \) Copy content Toggle raw display
$71$ \( T \) Copy content Toggle raw display
$73$ \( T - 8 \) Copy content Toggle raw display
$79$ \( T + 10 \) Copy content Toggle raw display
$83$ \( T + 6 \) Copy content Toggle raw display
$89$ \( T + 6 \) Copy content Toggle raw display
$97$ \( T + 10 \) Copy content Toggle raw display
show more
show less