Properties

Label 3025.2.a.a
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 11)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{2} + q^{3} + 2q^{4} - 2q^{6} - 2q^{7} - 2q^{9} + O(q^{10}) \) \( q - 2q^{2} + q^{3} + 2q^{4} - 2q^{6} - 2q^{7} - 2q^{9} + 2q^{12} + 4q^{13} + 4q^{14} - 4q^{16} - 2q^{17} + 4q^{18} - 2q^{21} + q^{23} - 8q^{26} - 5q^{27} - 4q^{28} + 7q^{31} + 8q^{32} + 4q^{34} - 4q^{36} - 3q^{37} + 4q^{39} + 8q^{41} + 4q^{42} - 6q^{43} - 2q^{46} - 8q^{47} - 4q^{48} - 3q^{49} - 2q^{51} + 8q^{52} + 6q^{53} + 10q^{54} + 5q^{59} - 12q^{61} - 14q^{62} + 4q^{63} - 8q^{64} + 7q^{67} - 4q^{68} + q^{69} - 3q^{71} + 4q^{73} + 6q^{74} - 8q^{78} + 10q^{79} + q^{81} - 16q^{82} - 6q^{83} - 4q^{84} + 12q^{86} + 15q^{89} - 8q^{91} + 2q^{92} + 7q^{93} + 16q^{94} + 8q^{96} + 7q^{97} + 6q^{98} + O(q^{100}) \)

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
−2.00000 1.00000 2.00000 0 −2.00000 −2.00000 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

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.a 1
5.b even 2 1 121.2.a.d 1
11.b odd 2 1 275.2.a.b 1
15.d odd 2 1 1089.2.a.b 1
20.d odd 2 1 1936.2.a.i 1
33.d even 2 1 2475.2.a.a 1
35.c odd 2 1 5929.2.a.h 1
40.e odd 2 1 7744.2.a.k 1
40.f even 2 1 7744.2.a.x 1
44.c even 2 1 4400.2.a.i 1
55.d odd 2 1 11.2.a.a 1
55.e even 4 2 275.2.b.a 2
55.h odd 10 4 121.2.c.e 4
55.j even 10 4 121.2.c.a 4
165.d even 2 1 99.2.a.d 1
165.l odd 4 2 2475.2.c.a 2
220.g even 2 1 176.2.a.b 1
220.i odd 4 2 4400.2.b.h 2
385.h even 2 1 539.2.a.a 1
385.o even 6 2 539.2.e.g 2
385.q odd 6 2 539.2.e.h 2
440.c even 2 1 704.2.a.c 1
440.o odd 2 1 704.2.a.h 1
495.o odd 6 2 891.2.e.k 2
495.r even 6 2 891.2.e.b 2
660.g odd 2 1 1584.2.a.g 1
715.c odd 2 1 1859.2.a.b 1
880.x odd 4 2 2816.2.c.j 2
880.bi even 4 2 2816.2.c.f 2
935.h odd 2 1 3179.2.a.a 1
1045.e even 2 1 3971.2.a.b 1
1155.e odd 2 1 4851.2.a.t 1
1265.f even 2 1 5819.2.a.a 1
1320.b odd 2 1 6336.2.a.bu 1
1320.u even 2 1 6336.2.a.br 1
1540.b odd 2 1 8624.2.a.j 1
1595.e odd 2 1 9251.2.a.d 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
11.2.a.a 1 55.d odd 2 1
99.2.a.d 1 165.d even 2 1
121.2.a.d 1 5.b even 2 1
121.2.c.a 4 55.j even 10 4
121.2.c.e 4 55.h odd 10 4
176.2.a.b 1 220.g even 2 1
275.2.a.b 1 11.b odd 2 1
275.2.b.a 2 55.e even 4 2
539.2.a.a 1 385.h even 2 1
539.2.e.g 2 385.o even 6 2
539.2.e.h 2 385.q odd 6 2
704.2.a.c 1 440.c even 2 1
704.2.a.h 1 440.o odd 2 1
891.2.e.b 2 495.r even 6 2
891.2.e.k 2 495.o odd 6 2
1089.2.a.b 1 15.d odd 2 1
1584.2.a.g 1 660.g odd 2 1
1859.2.a.b 1 715.c odd 2 1
1936.2.a.i 1 20.d odd 2 1
2475.2.a.a 1 33.d even 2 1
2475.2.c.a 2 165.l odd 4 2
2816.2.c.f 2 880.bi even 4 2
2816.2.c.j 2 880.x odd 4 2
3025.2.a.a 1 1.a even 1 1 trivial
3179.2.a.a 1 935.h odd 2 1
3971.2.a.b 1 1045.e even 2 1
4400.2.a.i 1 44.c even 2 1
4400.2.b.h 2 220.i odd 4 2
4851.2.a.t 1 1155.e odd 2 1
5819.2.a.a 1 1265.f even 2 1
5929.2.a.h 1 35.c odd 2 1
6336.2.a.br 1 1320.u even 2 1
6336.2.a.bu 1 1320.b odd 2 1
7744.2.a.k 1 40.e odd 2 1
7744.2.a.x 1 40.f even 2 1
8624.2.a.j 1 1540.b odd 2 1
9251.2.a.d 1 1595.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(3025))\):

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 2 + T \)
$3$ \( -1 + T \)
$5$ \( T \)
$7$ \( 2 + T \)
$11$ \( T \)
$13$ \( -4 + T \)
$17$ \( 2 + T \)
$19$ \( T \)
$23$ \( -1 + T \)
$29$ \( T \)
$31$ \( -7 + T \)
$37$ \( 3 + T \)
$41$ \( -8 + T \)
$43$ \( 6 + T \)
$47$ \( 8 + T \)
$53$ \( -6 + T \)
$59$ \( -5 + T \)
$61$ \( 12 + T \)
$67$ \( -7 + T \)
$71$ \( 3 + T \)
$73$ \( -4 + T \)
$79$ \( -10 + T \)
$83$ \( 6 + T \)
$89$ \( -15 + T \)
$97$ \( -7 + T \)
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