Properties

Label 1925.2.a.c
Level 1925
Weight 2
Character orbit 1925.a
Self dual yes
Analytic conductor 15.371
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1925.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.3712023891\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - 2q^{3} - q^{4} + 2q^{6} + q^{7} + 3q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - 2q^{3} - q^{4} + 2q^{6} + q^{7} + 3q^{8} + q^{9} + q^{11} + 2q^{12} - 4q^{13} - q^{14} - q^{16} - 4q^{17} - q^{18} - 2q^{21} - q^{22} + 4q^{23} - 6q^{24} + 4q^{26} + 4q^{27} - q^{28} - 6q^{29} + 10q^{31} - 5q^{32} - 2q^{33} + 4q^{34} - q^{36} + 6q^{37} + 8q^{39} + 4q^{41} + 2q^{42} - 12q^{43} - q^{44} - 4q^{46} + 10q^{47} + 2q^{48} + q^{49} + 8q^{51} + 4q^{52} + 6q^{53} - 4q^{54} + 3q^{56} + 6q^{58} + 2q^{59} - 10q^{62} + q^{63} + 7q^{64} + 2q^{66} - 8q^{67} + 4q^{68} - 8q^{69} - 12q^{71} + 3q^{72} + 8q^{73} - 6q^{74} + q^{77} - 8q^{78} + 8q^{79} - 11q^{81} - 4q^{82} + 2q^{84} + 12q^{86} + 12q^{87} + 3q^{88} - 6q^{89} - 4q^{91} - 4q^{92} - 20q^{93} - 10q^{94} + 10q^{96} + 10q^{97} - q^{98} + q^{99} + O(q^{100}) \)

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

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 1925.2.a.c 1
5.b even 2 1 77.2.a.c 1
5.c odd 4 2 1925.2.b.d 2
15.d odd 2 1 693.2.a.a 1
20.d odd 2 1 1232.2.a.a 1
35.c odd 2 1 539.2.a.d 1
35.i odd 6 2 539.2.e.b 2
35.j even 6 2 539.2.e.a 2
40.e odd 2 1 4928.2.a.bi 1
40.f even 2 1 4928.2.a.g 1
55.d odd 2 1 847.2.a.a 1
55.h odd 10 4 847.2.f.k 4
55.j even 10 4 847.2.f.e 4
105.g even 2 1 4851.2.a.a 1
140.c even 2 1 8624.2.a.bc 1
165.d even 2 1 7623.2.a.n 1
385.h even 2 1 5929.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
77.2.a.c 1 5.b even 2 1
539.2.a.d 1 35.c odd 2 1
539.2.e.a 2 35.j even 6 2
539.2.e.b 2 35.i odd 6 2
693.2.a.a 1 15.d odd 2 1
847.2.a.a 1 55.d odd 2 1
847.2.f.e 4 55.j even 10 4
847.2.f.k 4 55.h odd 10 4
1232.2.a.a 1 20.d odd 2 1
1925.2.a.c 1 1.a even 1 1 trivial
1925.2.b.d 2 5.c odd 4 2
4851.2.a.a 1 105.g even 2 1
4928.2.a.g 1 40.f even 2 1
4928.2.a.bi 1 40.e odd 2 1
5929.2.a.b 1 385.h even 2 1
7623.2.a.n 1 165.d even 2 1
8624.2.a.bc 1 140.c even 2 1

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(7\) \(-1\)
\(11\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1925))\):

\( T_{2} + 1 \)
\( T_{3} + 2 \)
\( T_{13} + 4 \)

Hecke characteristic polynomials

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