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

\(f(q)\) \(=\) \( q + 2 q^{2} - q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 3 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{2} - q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 3 q^{7} + q^{9} + 2 q^{10} - q^{11} - 2 q^{12} - q^{13} + 6 q^{14} - q^{15} - 4 q^{16} - q^{17} + 2 q^{18} - 2 q^{19} + 2 q^{20} - 3 q^{21} - 2 q^{22} - 3 q^{23} + q^{25} - 2 q^{26} - q^{27} + 6 q^{28} - 2 q^{29} - 2 q^{30} - 6 q^{31} - 8 q^{32} + q^{33} - 2 q^{34} + 3 q^{35} + 2 q^{36} + 11 q^{37} - 4 q^{38} + q^{39} - 5 q^{41} - 6 q^{42} + 4 q^{43} - 2 q^{44} + q^{45} - 6 q^{46} - 10 q^{47} + 4 q^{48} + 2 q^{49} + 2 q^{50} + q^{51} - 2 q^{52} + 11 q^{53} - 2 q^{54} - q^{55} + 2 q^{57} - 4 q^{58} + 8 q^{59} - 2 q^{60} + 13 q^{61} - 12 q^{62} + 3 q^{63} - 8 q^{64} - q^{65} + 2 q^{66} + 12 q^{67} - 2 q^{68} + 3 q^{69} + 6 q^{70} - 5 q^{71} + 10 q^{73} + 22 q^{74} - q^{75} - 4 q^{76} - 3 q^{77} + 2 q^{78} - 3 q^{79} - 4 q^{80} + q^{81} - 10 q^{82} - 12 q^{83} - 6 q^{84} - q^{85} + 8 q^{86} + 2 q^{87} - 15 q^{89} + 2 q^{90} - 3 q^{91} - 6 q^{92} + 6 q^{93} - 20 q^{94} - 2 q^{95} + 8 q^{96} + 17 q^{97} + 4 q^{98} - q^{99}+O(q^{100}) \) 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
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(195))\):

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

Hecke characteristic polynomials

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