Properties

Label 1805.2.a.b
Level $1805$
Weight $2$
Character orbit 1805.a
Self dual yes
Analytic conductor $14.413$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.4129975648\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2 q^{3} - 2 q^{4} - q^{5} - 4 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{3} - 2 q^{4} - q^{5} - 4 q^{7} + q^{9} + 3 q^{11} - 4 q^{12} - 2 q^{13} - 2 q^{15} + 4 q^{16} + 6 q^{17} + 2 q^{20} - 8 q^{21} + q^{25} - 4 q^{27} + 8 q^{28} + 3 q^{29} + 7 q^{31} + 6 q^{33} + 4 q^{35} - 2 q^{36} - 8 q^{37} - 4 q^{39} + 6 q^{41} - 4 q^{43} - 6 q^{44} - q^{45} + 6 q^{47} + 8 q^{48} + 9 q^{49} + 12 q^{51} + 4 q^{52} + 6 q^{53} - 3 q^{55} + 15 q^{59} + 4 q^{60} + 5 q^{61} - 4 q^{63} - 8 q^{64} + 2 q^{65} - 2 q^{67} - 12 q^{68} + 3 q^{71} + 8 q^{73} + 2 q^{75} - 12 q^{77} - 5 q^{79} - 4 q^{80} - 11 q^{81} + 12 q^{83} + 16 q^{84} - 6 q^{85} + 6 q^{87} + 15 q^{89} + 8 q^{91} + 14 q^{93} - 8 q^{97} + 3 q^{99}+O(q^{100}) \) 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 2.00000 −2.00000 −1.00000 0 −4.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(19\) \(-1\)

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 1805.2.a.b 1
5.b even 2 1 9025.2.a.e 1
19.b odd 2 1 1805.2.a.a 1
19.d odd 6 2 95.2.e.a 2
57.f even 6 2 855.2.k.b 2
76.f even 6 2 1520.2.q.c 2
95.d odd 2 1 9025.2.a.g 1
95.h odd 6 2 475.2.e.b 2
95.l even 12 4 475.2.j.a 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.2.e.a 2 19.d odd 6 2
475.2.e.b 2 95.h odd 6 2
475.2.j.a 4 95.l even 12 4
855.2.k.b 2 57.f even 6 2
1520.2.q.c 2 76.f even 6 2
1805.2.a.a 1 19.b odd 2 1
1805.2.a.b 1 1.a even 1 1 trivial
9025.2.a.e 1 5.b even 2 1
9025.2.a.g 1 95.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1805))\):

\( T_{2} \) Copy content Toggle raw display
\( T_{3} - 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T - 2 \) Copy content Toggle raw display
$5$ \( T + 1 \) Copy content Toggle raw display
$7$ \( T + 4 \) Copy content Toggle raw display
$11$ \( T - 3 \) Copy content Toggle raw display
$13$ \( T + 2 \) Copy content Toggle raw display
$17$ \( T - 6 \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T \) Copy content Toggle raw display
$29$ \( T - 3 \) Copy content Toggle raw display
$31$ \( T - 7 \) Copy content Toggle raw display
$37$ \( T + 8 \) Copy content Toggle raw display
$41$ \( T - 6 \) Copy content Toggle raw display
$43$ \( T + 4 \) Copy content Toggle raw display
$47$ \( T - 6 \) Copy content Toggle raw display
$53$ \( T - 6 \) Copy content Toggle raw display
$59$ \( T - 15 \) Copy content Toggle raw display
$61$ \( T - 5 \) Copy content Toggle raw display
$67$ \( T + 2 \) Copy content Toggle raw display
$71$ \( T - 3 \) Copy content Toggle raw display
$73$ \( T - 8 \) Copy content Toggle raw display
$79$ \( T + 5 \) Copy content Toggle raw display
$83$ \( T - 12 \) Copy content Toggle raw display
$89$ \( T - 15 \) Copy content Toggle raw display
$97$ \( T + 8 \) Copy content Toggle raw display
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