Properties

Label 195.2.a.b
Level $195$
Weight $2$
Character orbit 195.a
Self dual yes
Analytic conductor $1.557$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 195 = 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 195.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.55708283941\)
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

\(f(q)\) \(=\) \( q + 2q^{2} - q^{3} + 2q^{4} + q^{5} - 2q^{6} + 3q^{7} + q^{9} + O(q^{10}) \) \( q + 2q^{2} - q^{3} + 2q^{4} + q^{5} - 2q^{6} + 3q^{7} + q^{9} + 2q^{10} - q^{11} - 2q^{12} - q^{13} + 6q^{14} - q^{15} - 4q^{16} - q^{17} + 2q^{18} - 2q^{19} + 2q^{20} - 3q^{21} - 2q^{22} - 3q^{23} + q^{25} - 2q^{26} - q^{27} + 6q^{28} - 2q^{29} - 2q^{30} - 6q^{31} - 8q^{32} + q^{33} - 2q^{34} + 3q^{35} + 2q^{36} + 11q^{37} - 4q^{38} + q^{39} - 5q^{41} - 6q^{42} + 4q^{43} - 2q^{44} + q^{45} - 6q^{46} - 10q^{47} + 4q^{48} + 2q^{49} + 2q^{50} + q^{51} - 2q^{52} + 11q^{53} - 2q^{54} - q^{55} + 2q^{57} - 4q^{58} + 8q^{59} - 2q^{60} + 13q^{61} - 12q^{62} + 3q^{63} - 8q^{64} - q^{65} + 2q^{66} + 12q^{67} - 2q^{68} + 3q^{69} + 6q^{70} - 5q^{71} + 10q^{73} + 22q^{74} - q^{75} - 4q^{76} - 3q^{77} + 2q^{78} - 3q^{79} - 4q^{80} + q^{81} - 10q^{82} - 12q^{83} - 6q^{84} - q^{85} + 8q^{86} + 2q^{87} - 15q^{89} + 2q^{90} - 3q^{91} - 6q^{92} + 6q^{93} - 20q^{94} - 2q^{95} + 8q^{96} + 17q^{97} + 4q^{98} - q^{99} + O(q^{100}) \)

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
2.00000 −1.00000 2.00000 1.00000 −2.00000 3.00000 0 1.00000 2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(5\) \(-1\)
\(13\) \(1\)

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 195.2.a.b 1
3.b odd 2 1 585.2.a.b 1
4.b odd 2 1 3120.2.a.u 1
5.b even 2 1 975.2.a.c 1
5.c odd 4 2 975.2.c.a 2
7.b odd 2 1 9555.2.a.v 1
12.b even 2 1 9360.2.a.d 1
13.b even 2 1 2535.2.a.a 1
15.d odd 2 1 2925.2.a.q 1
15.e even 4 2 2925.2.c.c 2
39.d odd 2 1 7605.2.a.u 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
195.2.a.b 1 1.a even 1 1 trivial
585.2.a.b 1 3.b odd 2 1
975.2.a.c 1 5.b even 2 1
975.2.c.a 2 5.c odd 4 2
2535.2.a.a 1 13.b even 2 1
2925.2.a.q 1 15.d odd 2 1
2925.2.c.c 2 15.e even 4 2
3120.2.a.u 1 4.b odd 2 1
7605.2.a.u 1 39.d odd 2 1
9360.2.a.d 1 12.b even 2 1
9555.2.a.v 1 7.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(195))\):

\( T_{2} - 2 \)
\( T_{7} - 3 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -2 + T \)
$3$ \( 1 + T \)
$5$ \( -1 + T \)
$7$ \( -3 + T \)
$11$ \( 1 + T \)
$13$ \( 1 + T \)
$17$ \( 1 + T \)
$19$ \( 2 + T \)
$23$ \( 3 + T \)
$29$ \( 2 + T \)
$31$ \( 6 + T \)
$37$ \( -11 + T \)
$41$ \( 5 + T \)
$43$ \( -4 + T \)
$47$ \( 10 + T \)
$53$ \( -11 + T \)
$59$ \( -8 + T \)
$61$ \( -13 + T \)
$67$ \( -12 + T \)
$71$ \( 5 + T \)
$73$ \( -10 + T \)
$79$ \( 3 + T \)
$83$ \( 12 + T \)
$89$ \( 15 + T \)
$97$ \( -17 + T \)
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