Properties

Label 2448.2.a.p
Level 2448
Weight 2
Character orbit 2448.a
Self dual yes
Analytic conductor 19.547
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2448.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(19.5473784148\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 102)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{5} + O(q^{10}) \) \( q + 2q^{5} - 4q^{11} - 2q^{13} - q^{17} - 4q^{19} - q^{25} + 10q^{29} - 8q^{31} - 2q^{37} - 10q^{41} - 12q^{43} - 7q^{49} - 6q^{53} - 8q^{55} + 12q^{59} - 10q^{61} - 4q^{65} + 12q^{67} + 10q^{73} + 8q^{79} + 4q^{83} - 2q^{85} + 6q^{89} - 8q^{95} - 14q^{97} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(17\) \(1\)

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 2448.2.a.p 1
3.b odd 2 1 816.2.a.b 1
4.b odd 2 1 306.2.a.b 1
8.b even 2 1 9792.2.a.l 1
8.d odd 2 1 9792.2.a.k 1
12.b even 2 1 102.2.a.c 1
20.d odd 2 1 7650.2.a.ca 1
24.f even 2 1 3264.2.a.m 1
24.h odd 2 1 3264.2.a.bc 1
60.h even 2 1 2550.2.a.c 1
60.l odd 4 2 2550.2.d.m 2
68.d odd 2 1 5202.2.a.c 1
84.h odd 2 1 4998.2.a.be 1
204.h even 2 1 1734.2.a.j 1
204.l even 4 2 1734.2.b.b 2
204.p even 8 4 1734.2.f.e 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
102.2.a.c 1 12.b even 2 1
306.2.a.b 1 4.b odd 2 1
816.2.a.b 1 3.b odd 2 1
1734.2.a.j 1 204.h even 2 1
1734.2.b.b 2 204.l even 4 2
1734.2.f.e 4 204.p even 8 4
2448.2.a.p 1 1.a even 1 1 trivial
2550.2.a.c 1 60.h even 2 1
2550.2.d.m 2 60.l odd 4 2
3264.2.a.m 1 24.f even 2 1
3264.2.a.bc 1 24.h odd 2 1
4998.2.a.be 1 84.h odd 2 1
5202.2.a.c 1 68.d odd 2 1
7650.2.a.ca 1 20.d odd 2 1
9792.2.a.k 1 8.d odd 2 1
9792.2.a.l 1 8.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2448))\):

\( T_{5} - 2 \)
\( T_{7} \)
\( T_{11} + 4 \)
\( T_{19} + 4 \)
\( T_{23} \)

Hecke characteristic polynomials

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