Properties

Label 7605.2.a.p
Level $7605$
Weight $2$
Character orbit 7605.a
Self dual yes
Analytic conductor $60.726$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7605.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.7262307372\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 195)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{4} + q^{5} - 2 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} - q^{4} + q^{5} - 2 q^{7} - 3 q^{8} + q^{10} - 2 q^{14} - q^{16} + 2 q^{17} - 2 q^{19} - q^{20} - 8 q^{23} + q^{25} + 2 q^{28} - 2 q^{29} + 2 q^{31} + 5 q^{32} + 2 q^{34} - 2 q^{35} - 8 q^{37} - 2 q^{38} - 3 q^{40} - 2 q^{41} + 4 q^{43} - 8 q^{46} + 4 q^{47} - 3 q^{49} + q^{50} + 6 q^{53} + 6 q^{56} - 2 q^{58} + 12 q^{59} + 10 q^{61} + 2 q^{62} + 7 q^{64} + 6 q^{67} - 2 q^{68} - 2 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 2 q^{76} - 8 q^{79} - q^{80} - 2 q^{82} + 12 q^{83} + 2 q^{85} + 4 q^{86} - 6 q^{89} + 8 q^{92} + 4 q^{94} - 2 q^{95} - 16 q^{97} - 3 q^{98}+O(q^{100}) \) 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
1.00000 0 −1.00000 1.00000 0 −2.00000 −3.00000 0 1.00000
\(n\): 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 7605.2.a.p 1
3.b odd 2 1 2535.2.a.e 1
13.b even 2 1 7605.2.a.d 1
13.d odd 4 2 585.2.b.a 2
39.d odd 2 1 2535.2.a.l 1
39.f even 4 2 195.2.b.b 2
156.l odd 4 2 3120.2.g.a 2
195.j odd 4 2 975.2.h.a 2
195.n even 4 2 975.2.b.b 2
195.u odd 4 2 975.2.h.d 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
195.2.b.b 2 39.f even 4 2
585.2.b.a 2 13.d odd 4 2
975.2.b.b 2 195.n even 4 2
975.2.h.a 2 195.j odd 4 2
975.2.h.d 2 195.u odd 4 2
2535.2.a.e 1 3.b odd 2 1
2535.2.a.l 1 39.d odd 2 1
3120.2.g.a 2 156.l odd 4 2
7605.2.a.d 1 13.b even 2 1
7605.2.a.p 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7605))\):

\( T_{2} - 1 \) Copy content Toggle raw display
\( T_{7} + 2 \) Copy content Toggle raw display
\( T_{11} \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 1 \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 1 \) Copy content Toggle raw display
$7$ \( T + 2 \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T \) Copy content Toggle raw display
$17$ \( T - 2 \) Copy content Toggle raw display
$19$ \( T + 2 \) Copy content Toggle raw display
$23$ \( T + 8 \) Copy content Toggle raw display
$29$ \( T + 2 \) Copy content Toggle raw display
$31$ \( T - 2 \) Copy content Toggle raw display
$37$ \( T + 8 \) Copy content Toggle raw display
$41$ \( T + 2 \) Copy content Toggle raw display
$43$ \( T - 4 \) Copy content Toggle raw display
$47$ \( T - 4 \) Copy content Toggle raw display
$53$ \( T - 6 \) Copy content Toggle raw display
$59$ \( T - 12 \) Copy content Toggle raw display
$61$ \( T - 10 \) Copy content Toggle raw display
$67$ \( T - 6 \) Copy content Toggle raw display
$71$ \( T - 8 \) Copy content Toggle raw display
$73$ \( T - 16 \) Copy content Toggle raw display
$79$ \( T + 8 \) Copy content Toggle raw display
$83$ \( T - 12 \) Copy content Toggle raw display
$89$ \( T + 6 \) Copy content Toggle raw display
$97$ \( T + 16 \) Copy content Toggle raw display
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