Properties

Label 1850.2.a.m
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} - 2q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} - 2q^{9} + 3q^{11} + q^{12} - 6q^{13} - 4q^{14} + q^{16} - 3q^{17} - 2q^{18} - 3q^{19} - 4q^{21} + 3q^{22} - 2q^{23} + q^{24} - 6q^{26} - 5q^{27} - 4q^{28} + q^{32} + 3q^{33} - 3q^{34} - 2q^{36} + q^{37} - 3q^{38} - 6q^{39} - 3q^{41} - 4q^{42} + 4q^{43} + 3q^{44} - 2q^{46} - 4q^{47} + q^{48} + 9q^{49} - 3q^{51} - 6q^{52} + 2q^{53} - 5q^{54} - 4q^{56} - 3q^{57} - 12q^{59} + 12q^{61} + 8q^{63} + q^{64} + 3q^{66} - 9q^{67} - 3q^{68} - 2q^{69} - 2q^{71} - 2q^{72} + 9q^{73} + q^{74} - 3q^{76} - 12q^{77} - 6q^{78} - 2q^{79} + q^{81} - 3q^{82} + 7q^{83} - 4q^{84} + 4q^{86} + 3q^{88} - 3q^{89} + 24q^{91} - 2q^{92} - 4q^{94} + q^{96} - 2q^{97} + 9q^{98} - 6q^{99} + O(q^{100}) \)

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 1.00000 1.00000 0 1.00000 −4.00000 1.00000 −2.00000 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.m yes 1
5.b even 2 1 1850.2.a.c 1
5.c odd 4 2 1850.2.b.e 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1850.2.a.c 1 5.b even 2 1
1850.2.a.m yes 1 1.a even 1 1 trivial
1850.2.b.e 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1850))\):

\( T_{3} - 1 \)
\( T_{7} + 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( -1 + T \)
$5$ \( T \)
$7$ \( 4 + T \)
$11$ \( -3 + T \)
$13$ \( 6 + T \)
$17$ \( 3 + T \)
$19$ \( 3 + T \)
$23$ \( 2 + T \)
$29$ \( T \)
$31$ \( T \)
$37$ \( -1 + T \)
$41$ \( 3 + T \)
$43$ \( -4 + T \)
$47$ \( 4 + T \)
$53$ \( -2 + T \)
$59$ \( 12 + T \)
$61$ \( -12 + T \)
$67$ \( 9 + T \)
$71$ \( 2 + T \)
$73$ \( -9 + T \)
$79$ \( 2 + T \)
$83$ \( -7 + T \)
$89$ \( 3 + T \)
$97$ \( 2 + T \)
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