Properties

Label 1872.4.a.m
Level $1872$
Weight $4$
Character orbit 1872.a
Self dual yes
Analytic conductor $110.452$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1872.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(110.451575531\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 12 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q + 12 q^{5} - 2 q^{7} - 36 q^{11} + 13 q^{13} + 78 q^{17} - 74 q^{19} - 96 q^{23} + 19 q^{25} - 18 q^{29} + 214 q^{31} - 24 q^{35} - 286 q^{37} + 384 q^{41} - 524 q^{43} + 300 q^{47} - 339 q^{49} - 558 q^{53} - 432 q^{55} + 576 q^{59} + 74 q^{61} + 156 q^{65} - 38 q^{67} - 456 q^{71} - 682 q^{73} + 72 q^{77} - 704 q^{79} - 888 q^{83} + 936 q^{85} + 1020 q^{89} - 26 q^{91} - 888 q^{95} + 110 q^{97}+O(q^{100}) \) 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 0 0 12.0000 0 −2.00000 0 0 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 1872.4.a.m 1
3.b odd 2 1 624.4.a.g 1
4.b odd 2 1 117.4.a.a 1
12.b even 2 1 39.4.a.a 1
24.f even 2 1 2496.4.a.o 1
24.h odd 2 1 2496.4.a.f 1
52.b odd 2 1 1521.4.a.f 1
60.h even 2 1 975.4.a.e 1
84.h odd 2 1 1911.4.a.f 1
156.h even 2 1 507.4.a.c 1
156.l odd 4 2 507.4.b.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
39.4.a.a 1 12.b even 2 1
117.4.a.a 1 4.b odd 2 1
507.4.a.c 1 156.h even 2 1
507.4.b.b 2 156.l odd 4 2
624.4.a.g 1 3.b odd 2 1
975.4.a.e 1 60.h even 2 1
1521.4.a.f 1 52.b odd 2 1
1872.4.a.m 1 1.a even 1 1 trivial
1911.4.a.f 1 84.h odd 2 1
2496.4.a.f 1 24.h odd 2 1
2496.4.a.o 1 24.f even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1872))\):

\( T_{5} - 12 \) Copy content Toggle raw display
\( T_{7} + 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 12 \) Copy content Toggle raw display
$7$ \( T + 2 \) Copy content Toggle raw display
$11$ \( T + 36 \) Copy content Toggle raw display
$13$ \( T - 13 \) Copy content Toggle raw display
$17$ \( T - 78 \) Copy content Toggle raw display
$19$ \( T + 74 \) Copy content Toggle raw display
$23$ \( T + 96 \) Copy content Toggle raw display
$29$ \( T + 18 \) Copy content Toggle raw display
$31$ \( T - 214 \) Copy content Toggle raw display
$37$ \( T + 286 \) Copy content Toggle raw display
$41$ \( T - 384 \) Copy content Toggle raw display
$43$ \( T + 524 \) Copy content Toggle raw display
$47$ \( T - 300 \) Copy content Toggle raw display
$53$ \( T + 558 \) Copy content Toggle raw display
$59$ \( T - 576 \) Copy content Toggle raw display
$61$ \( T - 74 \) Copy content Toggle raw display
$67$ \( T + 38 \) Copy content Toggle raw display
$71$ \( T + 456 \) Copy content Toggle raw display
$73$ \( T + 682 \) Copy content Toggle raw display
$79$ \( T + 704 \) Copy content Toggle raw display
$83$ \( T + 888 \) Copy content Toggle raw display
$89$ \( T - 1020 \) Copy content Toggle raw display
$97$ \( T - 110 \) Copy content Toggle raw display
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