Properties

Label 96.2.a.a
Level $96$
Weight $2$
Character orbit 96.a
Self dual yes
Analytic conductor $0.767$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 96.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.766563859404\)
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: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} + 2q^{5} + 4q^{7} + q^{9} + O(q^{10}) \) \( q - q^{3} + 2q^{5} + 4q^{7} + q^{9} - 4q^{11} - 2q^{13} - 2q^{15} - 6q^{17} + 4q^{19} - 4q^{21} - q^{25} - q^{27} + 2q^{29} - 4q^{31} + 4q^{33} + 8q^{35} - 2q^{37} + 2q^{39} + 2q^{41} - 4q^{43} + 2q^{45} - 8q^{47} + 9q^{49} + 6q^{51} + 10q^{53} - 8q^{55} - 4q^{57} + 4q^{59} + 6q^{61} + 4q^{63} - 4q^{65} - 4q^{67} + 16q^{71} - 6q^{73} + q^{75} - 16q^{77} - 4q^{79} + q^{81} - 12q^{83} - 12q^{85} - 2q^{87} + 10q^{89} - 8q^{91} + 4q^{93} + 8q^{95} - 14q^{97} - 4q^{99} + O(q^{100}) \)

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 −1.00000 0 2.00000 0 4.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 96.2.a.a 1
3.b odd 2 1 288.2.a.c 1
4.b odd 2 1 96.2.a.b yes 1
5.b even 2 1 2400.2.a.r 1
5.c odd 4 2 2400.2.f.a 2
7.b odd 2 1 4704.2.a.t 1
8.b even 2 1 192.2.a.c 1
8.d odd 2 1 192.2.a.a 1
9.c even 3 2 2592.2.i.b 2
9.d odd 6 2 2592.2.i.q 2
12.b even 2 1 288.2.a.b 1
15.d odd 2 1 7200.2.a.e 1
15.e even 4 2 7200.2.f.x 2
16.e even 4 2 768.2.d.a 2
16.f odd 4 2 768.2.d.h 2
20.d odd 2 1 2400.2.a.q 1
20.e even 4 2 2400.2.f.r 2
24.f even 2 1 576.2.a.g 1
24.h odd 2 1 576.2.a.h 1
28.d even 2 1 4704.2.a.e 1
36.f odd 6 2 2592.2.i.h 2
36.h even 6 2 2592.2.i.w 2
40.e odd 2 1 4800.2.a.co 1
40.f even 2 1 4800.2.a.f 1
40.i odd 4 2 4800.2.f.bh 2
40.k even 4 2 4800.2.f.e 2
48.i odd 4 2 2304.2.d.c 2
48.k even 4 2 2304.2.d.s 2
56.e even 2 1 9408.2.a.ct 1
56.h odd 2 1 9408.2.a.bj 1
60.h even 2 1 7200.2.a.bx 1
60.l odd 4 2 7200.2.f.f 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
96.2.a.a 1 1.a even 1 1 trivial
96.2.a.b yes 1 4.b odd 2 1
192.2.a.a 1 8.d odd 2 1
192.2.a.c 1 8.b even 2 1
288.2.a.b 1 12.b even 2 1
288.2.a.c 1 3.b odd 2 1
576.2.a.g 1 24.f even 2 1
576.2.a.h 1 24.h odd 2 1
768.2.d.a 2 16.e even 4 2
768.2.d.h 2 16.f odd 4 2
2304.2.d.c 2 48.i odd 4 2
2304.2.d.s 2 48.k even 4 2
2400.2.a.q 1 20.d odd 2 1
2400.2.a.r 1 5.b even 2 1
2400.2.f.a 2 5.c odd 4 2
2400.2.f.r 2 20.e even 4 2
2592.2.i.b 2 9.c even 3 2
2592.2.i.h 2 36.f odd 6 2
2592.2.i.q 2 9.d odd 6 2
2592.2.i.w 2 36.h even 6 2
4704.2.a.e 1 28.d even 2 1
4704.2.a.t 1 7.b odd 2 1
4800.2.a.f 1 40.f even 2 1
4800.2.a.co 1 40.e odd 2 1
4800.2.f.e 2 40.k even 4 2
4800.2.f.bh 2 40.i odd 4 2
7200.2.a.e 1 15.d odd 2 1
7200.2.a.bx 1 60.h even 2 1
7200.2.f.f 2 60.l odd 4 2
7200.2.f.x 2 15.e even 4 2
9408.2.a.bj 1 56.h odd 2 1
9408.2.a.ct 1 56.e even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7} - 4 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(96))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 + T \)
$5$ \( 1 - 2 T + 5 T^{2} \)
$7$ \( 1 - 4 T + 7 T^{2} \)
$11$ \( 1 + 4 T + 11 T^{2} \)
$13$ \( 1 + 2 T + 13 T^{2} \)
$17$ \( 1 + 6 T + 17 T^{2} \)
$19$ \( 1 - 4 T + 19 T^{2} \)
$23$ \( 1 + 23 T^{2} \)
$29$ \( 1 - 2 T + 29 T^{2} \)
$31$ \( 1 + 4 T + 31 T^{2} \)
$37$ \( 1 + 2 T + 37 T^{2} \)
$41$ \( 1 - 2 T + 41 T^{2} \)
$43$ \( 1 + 4 T + 43 T^{2} \)
$47$ \( 1 + 8 T + 47 T^{2} \)
$53$ \( 1 - 10 T + 53 T^{2} \)
$59$ \( 1 - 4 T + 59 T^{2} \)
$61$ \( 1 - 6 T + 61 T^{2} \)
$67$ \( 1 + 4 T + 67 T^{2} \)
$71$ \( 1 - 16 T + 71 T^{2} \)
$73$ \( 1 + 6 T + 73 T^{2} \)
$79$ \( 1 + 4 T + 79 T^{2} \)
$83$ \( 1 + 12 T + 83 T^{2} \)
$89$ \( 1 - 10 T + 89 T^{2} \)
$97$ \( 1 + 14 T + 97 T^{2} \)
show more
show less