Properties

Label 2496.2.a.b
Level $2496$
Weight $2$
Character orbit 2496.a
Self dual yes
Analytic conductor $19.931$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2496.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(19.9306603445\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} - 2 q^{5} - 4 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{3} - 2 q^{5} - 4 q^{7} + q^{9} - 4 q^{11} - q^{13} + 2 q^{15} + 2 q^{17} - 8 q^{19} + 4 q^{21} - q^{25} - q^{27} - 6 q^{29} + 4 q^{31} + 4 q^{33} + 8 q^{35} + 2 q^{37} + q^{39} - 10 q^{41} + 4 q^{43} - 2 q^{45} - 8 q^{47} + 9 q^{49} - 2 q^{51} + 10 q^{53} + 8 q^{55} + 8 q^{57} + 4 q^{59} + 2 q^{61} - 4 q^{63} + 2 q^{65} - 16 q^{67} + 8 q^{71} + 2 q^{73} + q^{75} + 16 q^{77} - 8 q^{79} + q^{81} + 12 q^{83} - 4 q^{85} + 6 q^{87} + 14 q^{89} + 4 q^{91} - 4 q^{93} + 16 q^{95} + 10 q^{97} - 4 q^{99}+O(q^{100}) \) 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 −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
\(2\) \(-1\)
\(3\) \(1\)
\(13\) \(1\)

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 2496.2.a.b 1
3.b odd 2 1 7488.2.a.bk 1
4.b odd 2 1 2496.2.a.t 1
8.b even 2 1 624.2.a.h 1
8.d odd 2 1 78.2.a.a 1
12.b even 2 1 7488.2.a.bz 1
24.f even 2 1 234.2.a.c 1
24.h odd 2 1 1872.2.a.c 1
40.e odd 2 1 1950.2.a.w 1
40.k even 4 2 1950.2.e.i 2
56.e even 2 1 3822.2.a.j 1
72.l even 6 2 2106.2.e.j 2
72.p odd 6 2 2106.2.e.q 2
88.g even 2 1 9438.2.a.t 1
104.e even 2 1 8112.2.a.v 1
104.h odd 2 1 1014.2.a.d 1
104.m even 4 2 1014.2.b.b 2
104.n odd 6 2 1014.2.e.f 2
104.p odd 6 2 1014.2.e.c 2
104.u even 12 4 1014.2.i.d 4
120.m even 2 1 5850.2.a.d 1
120.q odd 4 2 5850.2.e.bb 2
312.h even 2 1 3042.2.a.f 1
312.w odd 4 2 3042.2.b.g 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
78.2.a.a 1 8.d odd 2 1
234.2.a.c 1 24.f even 2 1
624.2.a.h 1 8.b even 2 1
1014.2.a.d 1 104.h odd 2 1
1014.2.b.b 2 104.m even 4 2
1014.2.e.c 2 104.p odd 6 2
1014.2.e.f 2 104.n odd 6 2
1014.2.i.d 4 104.u even 12 4
1872.2.a.c 1 24.h odd 2 1
1950.2.a.w 1 40.e odd 2 1
1950.2.e.i 2 40.k even 4 2
2106.2.e.j 2 72.l even 6 2
2106.2.e.q 2 72.p odd 6 2
2496.2.a.b 1 1.a even 1 1 trivial
2496.2.a.t 1 4.b odd 2 1
3042.2.a.f 1 312.h even 2 1
3042.2.b.g 2 312.w odd 4 2
3822.2.a.j 1 56.e even 2 1
5850.2.a.d 1 120.m even 2 1
5850.2.e.bb 2 120.q odd 4 2
7488.2.a.bk 1 3.b odd 2 1
7488.2.a.bz 1 12.b even 2 1
8112.2.a.v 1 104.e even 2 1
9438.2.a.t 1 88.g even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2496))\):

\( T_{5} + 2 \) Copy content Toggle raw display
\( T_{7} + 4 \) Copy content Toggle raw display
\( T_{11} + 4 \) Copy content Toggle raw display
\( T_{17} - 2 \) Copy content Toggle raw display
\( T_{19} + 8 \) 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
$5$ \( T + 2 \) Copy content Toggle raw display
$7$ \( T + 4 \) Copy content Toggle raw display
$11$ \( T + 4 \) Copy content Toggle raw display
$13$ \( T + 1 \) Copy content Toggle raw display
$17$ \( T - 2 \) Copy content Toggle raw display
$19$ \( T + 8 \) Copy content Toggle raw display
$23$ \( T \) Copy content Toggle raw display
$29$ \( T + 6 \) Copy content Toggle raw display
$31$ \( T - 4 \) Copy content Toggle raw display
$37$ \( T - 2 \) Copy content Toggle raw display
$41$ \( T + 10 \) Copy content Toggle raw display
$43$ \( T - 4 \) Copy content Toggle raw display
$47$ \( T + 8 \) Copy content Toggle raw display
$53$ \( T - 10 \) Copy content Toggle raw display
$59$ \( T - 4 \) Copy content Toggle raw display
$61$ \( T - 2 \) Copy content Toggle raw display
$67$ \( T + 16 \) Copy content Toggle raw display
$71$ \( T - 8 \) Copy content Toggle raw display
$73$ \( T - 2 \) Copy content Toggle raw display
$79$ \( T + 8 \) Copy content Toggle raw display
$83$ \( T - 12 \) Copy content Toggle raw display
$89$ \( T - 14 \) Copy content Toggle raw display
$97$ \( T - 10 \) Copy content Toggle raw display
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