Properties

Label 1850.2.a.a
Level $1850$
Weight $2$
Character orbit 1850.a
Self dual yes
Analytic conductor $14.772$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1850.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.7723243739\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} - 4 q^{7} - q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} - 4 q^{7} - q^{8} + q^{9} - 2 q^{12} + 2 q^{13} + 4 q^{14} + q^{16} - q^{18} + 5 q^{19} + 8 q^{21} + 3 q^{23} + 2 q^{24} - 2 q^{26} + 4 q^{27} - 4 q^{28} + 6 q^{29} - 4 q^{31} - q^{32} + q^{36} + q^{37} - 5 q^{38} - 4 q^{39} - 9 q^{41} - 8 q^{42} - 7 q^{43} - 3 q^{46} - 6 q^{47} - 2 q^{48} + 9 q^{49} + 2 q^{52} + 9 q^{53} - 4 q^{54} + 4 q^{56} - 10 q^{57} - 6 q^{58} + 3 q^{59} + 2 q^{61} + 4 q^{62} - 4 q^{63} + q^{64} + 2 q^{67} - 6 q^{69} - 6 q^{71} - q^{72} + 11 q^{73} - q^{74} + 5 q^{76} + 4 q^{78} - q^{79} - 11 q^{81} + 9 q^{82} + 8 q^{84} + 7 q^{86} - 12 q^{87} - 6 q^{89} - 8 q^{91} + 3 q^{92} + 8 q^{93} + 6 q^{94} + 2 q^{96} - 4 q^{97} - 9 q^{98}+O(q^{100}) \) 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
−1.00000 −2.00000 1.00000 0 2.00000 −4.00000 −1.00000 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(5\) \(-1\)
\(37\) \(-1\)

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 1850.2.a.a 1
5.b even 2 1 1850.2.a.p yes 1
5.c odd 4 2 1850.2.b.f 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1850.2.a.a 1 1.a even 1 1 trivial
1850.2.a.p yes 1 5.b even 2 1
1850.2.b.f 2 5.c odd 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1850))\):

\( T_{3} + 2 \) Copy content Toggle raw display
\( T_{7} + 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 1 \) Copy content Toggle raw display
$3$ \( T + 2 \) Copy content Toggle raw display
$5$ \( T \) Copy content Toggle raw display
$7$ \( T + 4 \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T - 2 \) Copy content Toggle raw display
$17$ \( T \) Copy content Toggle raw display
$19$ \( T - 5 \) Copy content Toggle raw display
$23$ \( T - 3 \) Copy content Toggle raw display
$29$ \( T - 6 \) Copy content Toggle raw display
$31$ \( T + 4 \) Copy content Toggle raw display
$37$ \( T - 1 \) Copy content Toggle raw display
$41$ \( T + 9 \) Copy content Toggle raw display
$43$ \( T + 7 \) Copy content Toggle raw display
$47$ \( T + 6 \) Copy content Toggle raw display
$53$ \( T - 9 \) Copy content Toggle raw display
$59$ \( T - 3 \) Copy content Toggle raw display
$61$ \( T - 2 \) Copy content Toggle raw display
$67$ \( T - 2 \) Copy content Toggle raw display
$71$ \( T + 6 \) Copy content Toggle raw display
$73$ \( T - 11 \) Copy content Toggle raw display
$79$ \( T + 1 \) Copy content Toggle raw display
$83$ \( T \) Copy content Toggle raw display
$89$ \( T + 6 \) Copy content Toggle raw display
$97$ \( T + 4 \) Copy content Toggle raw display
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