Properties

Label 195.2.a.d
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

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

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

$p$ $F_p(T)$
$2$ \( -2 + T \)
$3$ \( -1 + T \)
$5$ \( -1 + T \)
$7$ \( 3 + T \)
$11$ \( 5 + T \)
$13$ \( -1 + T \)
$17$ \( -5 + T \)
$19$ \( -2 + T \)
$23$ \( 1 + T \)
$29$ \( -10 + T \)
$31$ \( 2 + T \)
$37$ \( 3 + T \)
$41$ \( 9 + T \)
$43$ \( 4 + T \)
$47$ \( -10 + T \)
$53$ \( -9 + T \)
$59$ \( T \)
$61$ \( 11 + T \)
$67$ \( 4 + T \)
$71$ \( -15 + T \)
$73$ \( -6 + T \)
$79$ \( 11 + T \)
$83$ \( -8 + T \)
$89$ \( 11 + T \)
$97$ \( 9 + T \)
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