Properties

Label 3025.2.a.b
Level $3025$
Weight $2$
Character orbit 3025.a
Self dual yes
Analytic conductor $24.155$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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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: \(0\)
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: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - 2q^{3} - q^{4} + 2q^{6} + 2q^{7} + 3q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - 2q^{3} - q^{4} + 2q^{6} + 2q^{7} + 3q^{8} + q^{9} + 2q^{12} - q^{13} - 2q^{14} - q^{16} + 5q^{17} - q^{18} + 6q^{19} - 4q^{21} - 2q^{23} - 6q^{24} + q^{26} + 4q^{27} - 2q^{28} + 9q^{29} - 2q^{31} - 5q^{32} - 5q^{34} - q^{36} + 3q^{37} - 6q^{38} + 2q^{39} - 5q^{41} + 4q^{42} + 2q^{46} - 2q^{47} + 2q^{48} - 3q^{49} - 10q^{51} + q^{52} - 9q^{53} - 4q^{54} + 6q^{56} - 12q^{57} - 9q^{58} + 8q^{59} + 6q^{61} + 2q^{62} + 2q^{63} + 7q^{64} - 2q^{67} - 5q^{68} + 4q^{69} + 12q^{71} + 3q^{72} + 2q^{73} - 3q^{74} - 6q^{76} - 2q^{78} - 10q^{79} - 11q^{81} + 5q^{82} - 6q^{83} + 4q^{84} - 18q^{87} - 9q^{89} - 2q^{91} + 2q^{92} + 4q^{93} + 2q^{94} + 10q^{96} + 13q^{97} + 3q^{98} + O(q^{100}) \)

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 −2.00000 −1.00000 0 2.00000 2.00000 3.00000 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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

Hecke kernels

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

\( T_{2} + 1 \)
\( T_{3} + 2 \)
\( T_{19} - 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( 2 + T \)
$5$ \( T \)
$7$ \( -2 + T \)
$11$ \( T \)
$13$ \( 1 + T \)
$17$ \( -5 + T \)
$19$ \( -6 + T \)
$23$ \( 2 + T \)
$29$ \( -9 + T \)
$31$ \( 2 + T \)
$37$ \( -3 + T \)
$41$ \( 5 + T \)
$43$ \( T \)
$47$ \( 2 + T \)
$53$ \( 9 + T \)
$59$ \( -8 + T \)
$61$ \( -6 + T \)
$67$ \( 2 + T \)
$71$ \( -12 + T \)
$73$ \( -2 + T \)
$79$ \( 10 + T \)
$83$ \( 6 + T \)
$89$ \( 9 + T \)
$97$ \( -13 + T \)
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