Properties

Label 1840.4.a.g
Level $1840$
Weight $4$
Character orbit 1840.a
Self dual yes
Analytic conductor $108.564$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1840.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(108.563514411\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 5 q^{3} - 5 q^{5} - 12 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 5 q^{3} - 5 q^{5} - 12 q^{7} - 2 q^{9} - 22 q^{11} + 19 q^{13} - 25 q^{15} + 96 q^{17} + 98 q^{19} - 60 q^{21} - 23 q^{23} + 25 q^{25} - 145 q^{27} - 227 q^{29} + 285 q^{31} - 110 q^{33} + 60 q^{35} - 398 q^{37} + 95 q^{39} + 271 q^{41} + 100 q^{43} + 10 q^{45} + 285 q^{47} - 199 q^{49} + 480 q^{51} + 18 q^{53} + 110 q^{55} + 490 q^{57} + 352 q^{59} - 478 q^{61} + 24 q^{63} - 95 q^{65} - 330 q^{67} - 115 q^{69} - 835 q^{71} - 1127 q^{73} + 125 q^{75} + 264 q^{77} - 322 q^{79} - 671 q^{81} - 572 q^{83} - 480 q^{85} - 1135 q^{87} - 504 q^{89} - 228 q^{91} + 1425 q^{93} - 490 q^{95} + 1712 q^{97} + 44 q^{99}+O(q^{100}) \) 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 5.00000 0 −5.00000 0 −12.0000 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(1\)
\(23\) \(1\)

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 1840.4.a.g 1
4.b odd 2 1 230.4.a.a 1
12.b even 2 1 2070.4.a.o 1
20.d odd 2 1 1150.4.a.i 1
20.e even 4 2 1150.4.b.h 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
230.4.a.a 1 4.b odd 2 1
1150.4.a.i 1 20.d odd 2 1
1150.4.b.h 2 20.e even 4 2
1840.4.a.g 1 1.a even 1 1 trivial
2070.4.a.o 1 12.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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1840))\):

\( T_{3} - 5 \) Copy content Toggle raw display
\( T_{7} + 12 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T - 5 \) Copy content Toggle raw display
$5$ \( T + 5 \) Copy content Toggle raw display
$7$ \( T + 12 \) Copy content Toggle raw display
$11$ \( T + 22 \) Copy content Toggle raw display
$13$ \( T - 19 \) Copy content Toggle raw display
$17$ \( T - 96 \) Copy content Toggle raw display
$19$ \( T - 98 \) Copy content Toggle raw display
$23$ \( T + 23 \) Copy content Toggle raw display
$29$ \( T + 227 \) Copy content Toggle raw display
$31$ \( T - 285 \) Copy content Toggle raw display
$37$ \( T + 398 \) Copy content Toggle raw display
$41$ \( T - 271 \) Copy content Toggle raw display
$43$ \( T - 100 \) Copy content Toggle raw display
$47$ \( T - 285 \) Copy content Toggle raw display
$53$ \( T - 18 \) Copy content Toggle raw display
$59$ \( T - 352 \) Copy content Toggle raw display
$61$ \( T + 478 \) Copy content Toggle raw display
$67$ \( T + 330 \) Copy content Toggle raw display
$71$ \( T + 835 \) Copy content Toggle raw display
$73$ \( T + 1127 \) Copy content Toggle raw display
$79$ \( T + 322 \) Copy content Toggle raw display
$83$ \( T + 572 \) Copy content Toggle raw display
$89$ \( T + 504 \) Copy content Toggle raw display
$97$ \( T - 1712 \) Copy content Toggle raw display
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