Properties

Label 190.2.a.c
Level $190$
Weight $2$
Character orbit 190.a
Self dual yes
Analytic conductor $1.517$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 190 = 2 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 190.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.51715763840\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - q^{7} + q^{8} - 2q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - q^{7} + q^{8} - 2q^{9} + q^{10} + q^{12} - q^{13} - q^{14} + q^{15} + q^{16} - 3q^{17} - 2q^{18} + q^{19} + q^{20} - q^{21} + 3q^{23} + q^{24} + q^{25} - q^{26} - 5q^{27} - q^{28} - 3q^{29} + q^{30} + 2q^{31} + q^{32} - 3q^{34} - q^{35} - 2q^{36} - 10q^{37} + q^{38} - q^{39} + q^{40} + 6q^{41} - q^{42} + 2q^{43} - 2q^{45} + 3q^{46} + q^{48} - 6q^{49} + q^{50} - 3q^{51} - q^{52} + 3q^{53} - 5q^{54} - q^{56} + q^{57} - 3q^{58} + 3q^{59} + q^{60} + 8q^{61} + 2q^{62} + 2q^{63} + q^{64} - q^{65} - 7q^{67} - 3q^{68} + 3q^{69} - q^{70} + 12q^{71} - 2q^{72} - 13q^{73} - 10q^{74} + q^{75} + q^{76} - q^{78} + 14q^{79} + q^{80} + q^{81} + 6q^{82} + 6q^{83} - q^{84} - 3q^{85} + 2q^{86} - 3q^{87} + 6q^{89} - 2q^{90} + q^{91} + 3q^{92} + 2q^{93} + q^{95} + q^{96} - 10q^{97} - 6q^{98} + O(q^{100}) \)

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 1.00000 1.00000 −1.00000 1.00000 −2.00000 1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(-1\)
\(19\) \(-1\)

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 190.2.a.c 1
3.b odd 2 1 1710.2.a.d 1
4.b odd 2 1 1520.2.a.d 1
5.b even 2 1 950.2.a.a 1
5.c odd 4 2 950.2.b.e 2
7.b odd 2 1 9310.2.a.o 1
8.b even 2 1 6080.2.a.h 1
8.d odd 2 1 6080.2.a.p 1
15.d odd 2 1 8550.2.a.bd 1
19.b odd 2 1 3610.2.a.b 1
20.d odd 2 1 7600.2.a.m 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
190.2.a.c 1 1.a even 1 1 trivial
950.2.a.a 1 5.b even 2 1
950.2.b.e 2 5.c odd 4 2
1520.2.a.d 1 4.b odd 2 1
1710.2.a.d 1 3.b odd 2 1
3610.2.a.b 1 19.b odd 2 1
6080.2.a.h 1 8.b even 2 1
6080.2.a.p 1 8.d odd 2 1
7600.2.a.m 1 20.d odd 2 1
8550.2.a.bd 1 15.d odd 2 1
9310.2.a.o 1 7.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(190))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( -1 + T \)
$5$ \( -1 + T \)
$7$ \( 1 + T \)
$11$ \( T \)
$13$ \( 1 + T \)
$17$ \( 3 + T \)
$19$ \( -1 + T \)
$23$ \( -3 + T \)
$29$ \( 3 + T \)
$31$ \( -2 + T \)
$37$ \( 10 + T \)
$41$ \( -6 + T \)
$43$ \( -2 + T \)
$47$ \( T \)
$53$ \( -3 + T \)
$59$ \( -3 + T \)
$61$ \( -8 + T \)
$67$ \( 7 + T \)
$71$ \( -12 + T \)
$73$ \( 13 + T \)
$79$ \( -14 + T \)
$83$ \( -6 + T \)
$89$ \( -6 + T \)
$97$ \( 10 + T \)
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