Properties

Label 7605.2.a.a
Level $7605$
Weight $2$
Character orbit 7605.a
Self dual yes
Analytic conductor $60.726$
Analytic rank $1$
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: \(1\)
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

\(f(q)\) \(=\) \( q - 2 q^{2} + 2 q^{4} + q^{5} + 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{2} + 2 q^{4} + q^{5} + 5 q^{7} - 2 q^{10} - 2 q^{11} - 10 q^{14} - 4 q^{16} - 2 q^{17} + 2 q^{20} + 4 q^{22} - 6 q^{23} + q^{25} + 10 q^{28} + 4 q^{29} - 7 q^{31} + 8 q^{32} + 4 q^{34} + 5 q^{35} - 2 q^{37} - 6 q^{41} + q^{43} - 4 q^{44} + 12 q^{46} + 8 q^{47} + 18 q^{49} - 2 q^{50} + 4 q^{53} - 2 q^{55} - 8 q^{58} - 12 q^{59} - 13 q^{61} + 14 q^{62} - 8 q^{64} - 7 q^{67} - 4 q^{68} - 10 q^{70} - 12 q^{71} + 15 q^{73} + 4 q^{74} - 10 q^{77} + 3 q^{79} - 4 q^{80} + 12 q^{82} - 8 q^{83} - 2 q^{85} - 2 q^{86} - 14 q^{89} - 12 q^{92} - 16 q^{94} - 5 q^{97} - 36 q^{98}+O(q^{100}) \) 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
−2.00000 0 2.00000 1.00000 0 5.00000 0 0 −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 7605.2.a.a 1
3.b odd 2 1 2535.2.a.m 1
13.b even 2 1 7605.2.a.s 1
13.c even 3 2 585.2.j.b 2
39.d odd 2 1 2535.2.a.c 1
39.i odd 6 2 195.2.i.a 2
195.x odd 6 2 975.2.i.i 2
195.bl even 12 4 975.2.bb.f 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
195.2.i.a 2 39.i odd 6 2
585.2.j.b 2 13.c even 3 2
975.2.i.i 2 195.x odd 6 2
975.2.bb.f 4 195.bl even 12 4
2535.2.a.c 1 39.d odd 2 1
2535.2.a.m 1 3.b odd 2 1
7605.2.a.a 1 1.a even 1 1 trivial
7605.2.a.s 1 13.b even 2 1

Hecke kernels

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

\( T_{2} + 2 \) Copy content Toggle raw display
\( T_{7} - 5 \) Copy content Toggle raw display
\( T_{11} + 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 2 \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 1 \) Copy content Toggle raw display
$7$ \( T - 5 \) Copy content Toggle raw display
$11$ \( T + 2 \) Copy content Toggle raw display
$13$ \( T \) Copy content Toggle raw display
$17$ \( T + 2 \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T + 6 \) Copy content Toggle raw display
$29$ \( T - 4 \) Copy content Toggle raw display
$31$ \( T + 7 \) Copy content Toggle raw display
$37$ \( T + 2 \) Copy content Toggle raw display
$41$ \( T + 6 \) Copy content Toggle raw display
$43$ \( T - 1 \) Copy content Toggle raw display
$47$ \( T - 8 \) Copy content Toggle raw display
$53$ \( T - 4 \) Copy content Toggle raw display
$59$ \( T + 12 \) Copy content Toggle raw display
$61$ \( T + 13 \) Copy content Toggle raw display
$67$ \( T + 7 \) Copy content Toggle raw display
$71$ \( T + 12 \) Copy content Toggle raw display
$73$ \( T - 15 \) Copy content Toggle raw display
$79$ \( T - 3 \) Copy content Toggle raw display
$83$ \( T + 8 \) Copy content Toggle raw display
$89$ \( T + 14 \) Copy content Toggle raw display
$97$ \( T + 5 \) Copy content Toggle raw display
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