Properties

Label 1800.4.a.bd
Level $1800$
Weight $4$
Character orbit 1800.a
Self dual yes
Analytic conductor $106.203$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(106.203438010\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 40)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 18 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q + 18 q^{7} + 16 q^{11} + 6 q^{13} - 6 q^{17} - 124 q^{19} + 42 q^{23} - 142 q^{29} - 188 q^{31} - 202 q^{37} - 54 q^{41} - 66 q^{43} + 38 q^{47} - 19 q^{49} + 738 q^{53} - 564 q^{59} - 262 q^{61} + 554 q^{67} - 140 q^{71} - 882 q^{73} + 288 q^{77} - 1160 q^{79} + 642 q^{83} + 854 q^{89} + 108 q^{91} + 478 q^{97}+O(q^{100}) \) 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 0 0 18.0000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)
\(5\) \(1\)

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 1800.4.a.bd 1
3.b odd 2 1 200.4.a.a 1
5.b even 2 1 360.4.a.i 1
5.c odd 4 2 1800.4.f.n 2
12.b even 2 1 400.4.a.u 1
15.d odd 2 1 40.4.a.c 1
15.e even 4 2 200.4.c.a 2
20.d odd 2 1 720.4.a.ba 1
24.f even 2 1 1600.4.a.a 1
24.h odd 2 1 1600.4.a.ca 1
60.h even 2 1 80.4.a.a 1
60.l odd 4 2 400.4.c.a 2
105.g even 2 1 1960.4.a.a 1
120.i odd 2 1 320.4.a.a 1
120.m even 2 1 320.4.a.n 1
240.t even 4 2 1280.4.d.b 2
240.bm odd 4 2 1280.4.d.o 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
40.4.a.c 1 15.d odd 2 1
80.4.a.a 1 60.h even 2 1
200.4.a.a 1 3.b odd 2 1
200.4.c.a 2 15.e even 4 2
320.4.a.a 1 120.i odd 2 1
320.4.a.n 1 120.m even 2 1
360.4.a.i 1 5.b even 2 1
400.4.a.u 1 12.b even 2 1
400.4.c.a 2 60.l odd 4 2
720.4.a.ba 1 20.d odd 2 1
1280.4.d.b 2 240.t even 4 2
1280.4.d.o 2 240.bm odd 4 2
1600.4.a.a 1 24.f even 2 1
1600.4.a.ca 1 24.h odd 2 1
1800.4.a.bd 1 1.a even 1 1 trivial
1800.4.f.n 2 5.c odd 4 2
1960.4.a.a 1 105.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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1800))\):

\( T_{7} - 18 \) Copy content Toggle raw display
\( T_{11} - 16 \) Copy content Toggle raw display
\( T_{17} + 6 \) 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
$5$ \( T \) Copy content Toggle raw display
$7$ \( T - 18 \) Copy content Toggle raw display
$11$ \( T - 16 \) Copy content Toggle raw display
$13$ \( T - 6 \) Copy content Toggle raw display
$17$ \( T + 6 \) Copy content Toggle raw display
$19$ \( T + 124 \) Copy content Toggle raw display
$23$ \( T - 42 \) Copy content Toggle raw display
$29$ \( T + 142 \) Copy content Toggle raw display
$31$ \( T + 188 \) Copy content Toggle raw display
$37$ \( T + 202 \) Copy content Toggle raw display
$41$ \( T + 54 \) Copy content Toggle raw display
$43$ \( T + 66 \) Copy content Toggle raw display
$47$ \( T - 38 \) Copy content Toggle raw display
$53$ \( T - 738 \) Copy content Toggle raw display
$59$ \( T + 564 \) Copy content Toggle raw display
$61$ \( T + 262 \) Copy content Toggle raw display
$67$ \( T - 554 \) Copy content Toggle raw display
$71$ \( T + 140 \) Copy content Toggle raw display
$73$ \( T + 882 \) Copy content Toggle raw display
$79$ \( T + 1160 \) Copy content Toggle raw display
$83$ \( T - 642 \) Copy content Toggle raw display
$89$ \( T - 854 \) Copy content Toggle raw display
$97$ \( T - 478 \) Copy content Toggle raw display
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