Properties

Label 576.6.a.u
Level $576$
Weight $6$
Character orbit 576.a
Self dual yes
Analytic conductor $92.381$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 576.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(92.3810802123\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 32)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 14q^{5} - 208q^{7} + O(q^{10}) \) \( q + 14q^{5} - 208q^{7} - 536q^{11} - 694q^{13} + 1278q^{17} - 1112q^{19} - 3216q^{23} - 2929q^{25} + 2918q^{29} - 2624q^{31} - 2912q^{35} + 9458q^{37} - 170q^{41} + 19928q^{43} - 32q^{47} + 26457q^{49} - 22178q^{53} - 7504q^{55} + 41480q^{59} - 15462q^{61} - 9716q^{65} + 20744q^{67} - 28592q^{71} - 53670q^{73} + 111488q^{77} - 69152q^{79} - 37800q^{83} + 17892q^{85} + 126806q^{89} + 144352q^{91} - 15568q^{95} + 62290q^{97} + O(q^{100}) \)

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 14.0000 0 −208.000 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

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 576.6.a.u 1
3.b odd 2 1 64.6.a.e 1
4.b odd 2 1 576.6.a.v 1
8.b even 2 1 288.6.a.d 1
8.d odd 2 1 288.6.a.e 1
12.b even 2 1 64.6.a.c 1
24.f even 2 1 32.6.a.c yes 1
24.h odd 2 1 32.6.a.a 1
48.i odd 4 2 256.6.b.h 2
48.k even 4 2 256.6.b.b 2
120.i odd 2 1 800.6.a.e 1
120.m even 2 1 800.6.a.a 1
120.q odd 4 2 800.6.c.b 2
120.w even 4 2 800.6.c.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
32.6.a.a 1 24.h odd 2 1
32.6.a.c yes 1 24.f even 2 1
64.6.a.c 1 12.b even 2 1
64.6.a.e 1 3.b odd 2 1
256.6.b.b 2 48.k even 4 2
256.6.b.h 2 48.i odd 4 2
288.6.a.d 1 8.b even 2 1
288.6.a.e 1 8.d odd 2 1
576.6.a.u 1 1.a even 1 1 trivial
576.6.a.v 1 4.b odd 2 1
800.6.a.a 1 120.m even 2 1
800.6.a.e 1 120.i odd 2 1
800.6.c.a 2 120.w even 4 2
800.6.c.b 2 120.q odd 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(576))\):

\( T_{5} - 14 \)
\( T_{7} + 208 \)
\( T_{11} + 536 \)