Properties

Label 3025.2.a.d
Level $3025$
Weight $2$
Character orbit 3025.a
Self dual yes
Analytic conductor $24.155$
Analytic rank $1$
Dimension $1$
CM discriminant -11
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3025 = 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(24.1547466114\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 121)
Fricke sign: \(1\)
Sato-Tate group: $N(\mathrm{U}(1))$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} - 2 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{3} - 2 q^{4} - 2 q^{9} - 2 q^{12} + 4 q^{16} + 9 q^{23} - 5 q^{27} - 5 q^{31} + 4 q^{36} - 7 q^{37} + 12 q^{47} + 4 q^{48} - 7 q^{49} - 6 q^{53} - 15 q^{59} - 8 q^{64} - 13 q^{67} + 9 q^{69} - 3 q^{71} + q^{81} - 9 q^{89} - 18 q^{92} - 5 q^{93} - 17 q^{97}+O(q^{100}) \) 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 1.00000 −2.00000 0 0 0 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(11\) \(1\)

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.b odd 2 1 CM by \(\Q(\sqrt{-11}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 3025.2.a.d 1
5.b even 2 1 121.2.a.b 1
11.b odd 2 1 CM 3025.2.a.d 1
15.d odd 2 1 1089.2.a.g 1
20.d odd 2 1 1936.2.a.h 1
35.c odd 2 1 5929.2.a.e 1
40.e odd 2 1 7744.2.a.n 1
40.f even 2 1 7744.2.a.bb 1
55.d odd 2 1 121.2.a.b 1
55.h odd 10 4 121.2.c.c 4
55.j even 10 4 121.2.c.c 4
165.d even 2 1 1089.2.a.g 1
220.g even 2 1 1936.2.a.h 1
385.h even 2 1 5929.2.a.e 1
440.c even 2 1 7744.2.a.n 1
440.o odd 2 1 7744.2.a.bb 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
121.2.a.b 1 5.b even 2 1
121.2.a.b 1 55.d odd 2 1
121.2.c.c 4 55.h odd 10 4
121.2.c.c 4 55.j even 10 4
1089.2.a.g 1 15.d odd 2 1
1089.2.a.g 1 165.d even 2 1
1936.2.a.h 1 20.d odd 2 1
1936.2.a.h 1 220.g even 2 1
3025.2.a.d 1 1.a even 1 1 trivial
3025.2.a.d 1 11.b odd 2 1 CM
5929.2.a.e 1 35.c odd 2 1
5929.2.a.e 1 385.h even 2 1
7744.2.a.n 1 40.e odd 2 1
7744.2.a.n 1 440.c even 2 1
7744.2.a.bb 1 40.f even 2 1
7744.2.a.bb 1 440.o odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3025))\):

\( T_{2} \) Copy content Toggle raw display
\( T_{3} - 1 \) Copy content Toggle raw display
\( T_{19} \) Copy content Toggle raw display

Hecke characteristic polynomials

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