Properties

Label 7605.2.a.m
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 585)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2 q^{4} + q^{5} + q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{4} + q^{5} + q^{7} - 3 q^{11} + 4 q^{16} + 3 q^{17} + 4 q^{19} - 2 q^{20} + 9 q^{23} + q^{25} - 2 q^{28} + 6 q^{29} - 2 q^{31} + q^{35} + q^{37} - 3 q^{41} + 2 q^{43} + 6 q^{44} - 6 q^{47} - 6 q^{49} - 9 q^{53} - 3 q^{55} - 12 q^{59} + 5 q^{61} - 8 q^{64} + 4 q^{67} - 6 q^{68} + 9 q^{71} - 14 q^{73} - 8 q^{76} - 3 q^{77} - 7 q^{79} + 4 q^{80} + 3 q^{85} + 15 q^{89} - 18 q^{92} + 4 q^{95} - 5 q^{97}+O(q^{100}) \) 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
0 0 −2.00000 1.00000 0 1.00000 0 0 0
\(n\): 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.m 1
3.b odd 2 1 7605.2.a.j 1
13.b even 2 1 585.2.a.e 1
39.d odd 2 1 585.2.a.f yes 1
52.b odd 2 1 9360.2.a.r 1
65.d even 2 1 2925.2.a.k 1
65.h odd 4 2 2925.2.c.m 2
156.h even 2 1 9360.2.a.bu 1
195.e odd 2 1 2925.2.a.i 1
195.s even 4 2 2925.2.c.l 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
585.2.a.e 1 13.b even 2 1
585.2.a.f yes 1 39.d odd 2 1
2925.2.a.i 1 195.e odd 2 1
2925.2.a.k 1 65.d even 2 1
2925.2.c.l 2 195.s even 4 2
2925.2.c.m 2 65.h odd 4 2
7605.2.a.j 1 3.b odd 2 1
7605.2.a.m 1 1.a even 1 1 trivial
9360.2.a.r 1 52.b odd 2 1
9360.2.a.bu 1 156.h even 2 1

Hecke kernels

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

\( T_{2} \) Copy content Toggle raw display
\( T_{7} - 1 \) Copy content Toggle raw display
\( T_{11} + 3 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 1 \) Copy content Toggle raw display
$7$ \( T - 1 \) Copy content Toggle raw display
$11$ \( T + 3 \) Copy content Toggle raw display
$13$ \( T \) Copy content Toggle raw display
$17$ \( T - 3 \) Copy content Toggle raw display
$19$ \( T - 4 \) Copy content Toggle raw display
$23$ \( T - 9 \) Copy content Toggle raw display
$29$ \( T - 6 \) Copy content Toggle raw display
$31$ \( T + 2 \) Copy content Toggle raw display
$37$ \( T - 1 \) Copy content Toggle raw display
$41$ \( T + 3 \) Copy content Toggle raw display
$43$ \( T - 2 \) Copy content Toggle raw display
$47$ \( T + 6 \) Copy content Toggle raw display
$53$ \( T + 9 \) Copy content Toggle raw display
$59$ \( T + 12 \) Copy content Toggle raw display
$61$ \( T - 5 \) Copy content Toggle raw display
$67$ \( T - 4 \) Copy content Toggle raw display
$71$ \( T - 9 \) Copy content Toggle raw display
$73$ \( T + 14 \) Copy content Toggle raw display
$79$ \( T + 7 \) Copy content Toggle raw display
$83$ \( T \) Copy content Toggle raw display
$89$ \( T - 15 \) Copy content Toggle raw display
$97$ \( T + 5 \) Copy content Toggle raw display
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