Properties

Label 8464.2.a.b
Level $8464$
Weight $2$
Character orbit 8464.a
Self dual yes
Analytic conductor $67.585$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 8464 = 2^{4} \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8464.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(67.5853802708\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 184)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 3 q^{3} - 2 q^{7} + 6 q^{9} + O(q^{10}) \) \( q - 3 q^{3} - 2 q^{7} + 6 q^{9} - 5 q^{13} + 6 q^{17} + 6 q^{19} + 6 q^{21} - 5 q^{25} - 9 q^{27} + 9 q^{29} - 3 q^{31} + 8 q^{37} + 15 q^{39} + 3 q^{41} - 8 q^{43} - 7 q^{47} - 3 q^{49} - 18 q^{51} + 2 q^{53} - 18 q^{57} - 4 q^{59} + 10 q^{61} - 12 q^{63} + 8 q^{67} - 7 q^{71} + 9 q^{73} + 15 q^{75} - 6 q^{79} + 9 q^{81} - 14 q^{83} - 27 q^{87} - 16 q^{89} + 10 q^{91} + 9 q^{93} - 6 q^{97} + O(q^{100}) \)

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 −3.00000 0 0 0 −2.00000 0 6.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(23\) \(-1\)

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 8464.2.a.b 1
4.b odd 2 1 4232.2.a.j 1
23.b odd 2 1 368.2.a.a 1
69.c even 2 1 3312.2.a.i 1
92.b even 2 1 184.2.a.d 1
115.c odd 2 1 9200.2.a.bj 1
184.e odd 2 1 1472.2.a.m 1
184.h even 2 1 1472.2.a.a 1
276.h odd 2 1 1656.2.a.c 1
460.g even 2 1 4600.2.a.a 1
460.k odd 4 2 4600.2.e.a 2
644.h odd 2 1 9016.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
184.2.a.d 1 92.b even 2 1
368.2.a.a 1 23.b odd 2 1
1472.2.a.a 1 184.h even 2 1
1472.2.a.m 1 184.e odd 2 1
1656.2.a.c 1 276.h odd 2 1
3312.2.a.i 1 69.c even 2 1
4232.2.a.j 1 4.b odd 2 1
4600.2.a.a 1 460.g even 2 1
4600.2.e.a 2 460.k odd 4 2
8464.2.a.b 1 1.a even 1 1 trivial
9016.2.a.b 1 644.h odd 2 1
9200.2.a.bj 1 115.c odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8464))\):

\( T_{3} + 3 \)
\( T_{5} \)
\( T_{7} + 2 \)
\( T_{13} + 5 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 3 + T \)
$5$ \( T \)
$7$ \( 2 + T \)
$11$ \( T \)
$13$ \( 5 + T \)
$17$ \( -6 + T \)
$19$ \( -6 + T \)
$23$ \( T \)
$29$ \( -9 + T \)
$31$ \( 3 + T \)
$37$ \( -8 + T \)
$41$ \( -3 + T \)
$43$ \( 8 + T \)
$47$ \( 7 + T \)
$53$ \( -2 + T \)
$59$ \( 4 + T \)
$61$ \( -10 + T \)
$67$ \( -8 + T \)
$71$ \( 7 + T \)
$73$ \( -9 + T \)
$79$ \( 6 + T \)
$83$ \( 14 + T \)
$89$ \( 16 + T \)
$97$ \( 6 + T \)
show more
show less