Properties

Label 275.2.a.b
Level $275$
Weight $2$
Character orbit 275.a
Self dual yes
Analytic conductor $2.196$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 275.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(2.19588605559\)
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

\(f(q)\) \(=\) \( q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{7} - 2 q^{9} + q^{11} + 2 q^{12} - 4 q^{13} + 4 q^{14} - 4 q^{16} + 2 q^{17} - 4 q^{18} + 2 q^{21} + 2 q^{22} + q^{23} - 8 q^{26} - 5 q^{27} + 4 q^{28} + 7 q^{31} - 8 q^{32} + q^{33} + 4 q^{34} - 4 q^{36} - 3 q^{37} - 4 q^{39} - 8 q^{41} + 4 q^{42} + 6 q^{43} + 2 q^{44} + 2 q^{46} - 8 q^{47} - 4 q^{48} - 3 q^{49} + 2 q^{51} - 8 q^{52} + 6 q^{53} - 10 q^{54} + 5 q^{59} + 12 q^{61} + 14 q^{62} - 4 q^{63} - 8 q^{64} + 2 q^{66} + 7 q^{67} + 4 q^{68} + q^{69} - 3 q^{71} - 4 q^{73} - 6 q^{74} + 2 q^{77} - 8 q^{78} - 10 q^{79} + q^{81} - 16 q^{82} + 6 q^{83} + 4 q^{84} + 12 q^{86} + 15 q^{89} - 8 q^{91} + 2 q^{92} + 7 q^{93} - 16 q^{94} - 8 q^{96} + 7 q^{97} - 6 q^{98} - 2 q^{99} + O(q^{100}) \)

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
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 275.2.a.b 1
3.b odd 2 1 2475.2.a.a 1
4.b odd 2 1 4400.2.a.i 1
5.b even 2 1 11.2.a.a 1
5.c odd 4 2 275.2.b.a 2
11.b odd 2 1 3025.2.a.a 1
15.d odd 2 1 99.2.a.d 1
15.e even 4 2 2475.2.c.a 2
20.d odd 2 1 176.2.a.b 1
20.e even 4 2 4400.2.b.h 2
35.c odd 2 1 539.2.a.a 1
35.i odd 6 2 539.2.e.g 2
35.j even 6 2 539.2.e.h 2
40.e odd 2 1 704.2.a.c 1
40.f even 2 1 704.2.a.h 1
45.h odd 6 2 891.2.e.b 2
45.j even 6 2 891.2.e.k 2
55.d odd 2 1 121.2.a.d 1
55.h odd 10 4 121.2.c.a 4
55.j even 10 4 121.2.c.e 4
60.h even 2 1 1584.2.a.g 1
65.d even 2 1 1859.2.a.b 1
80.k odd 4 2 2816.2.c.f 2
80.q even 4 2 2816.2.c.j 2
85.c even 2 1 3179.2.a.a 1
95.d odd 2 1 3971.2.a.b 1
105.g even 2 1 4851.2.a.t 1
115.c odd 2 1 5819.2.a.a 1
120.i odd 2 1 6336.2.a.br 1
120.m even 2 1 6336.2.a.bu 1
140.c even 2 1 8624.2.a.j 1
145.d even 2 1 9251.2.a.d 1
165.d even 2 1 1089.2.a.b 1
220.g even 2 1 1936.2.a.i 1
385.h even 2 1 5929.2.a.h 1
440.c even 2 1 7744.2.a.k 1
440.o odd 2 1 7744.2.a.x 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
11.2.a.a 1 5.b even 2 1
99.2.a.d 1 15.d odd 2 1
121.2.a.d 1 55.d odd 2 1
121.2.c.a 4 55.h odd 10 4
121.2.c.e 4 55.j even 10 4
176.2.a.b 1 20.d odd 2 1
275.2.a.b 1 1.a even 1 1 trivial
275.2.b.a 2 5.c odd 4 2
539.2.a.a 1 35.c odd 2 1
539.2.e.g 2 35.i odd 6 2
539.2.e.h 2 35.j even 6 2
704.2.a.c 1 40.e odd 2 1
704.2.a.h 1 40.f even 2 1
891.2.e.b 2 45.h odd 6 2
891.2.e.k 2 45.j even 6 2
1089.2.a.b 1 165.d even 2 1
1584.2.a.g 1 60.h even 2 1
1859.2.a.b 1 65.d even 2 1
1936.2.a.i 1 220.g even 2 1
2475.2.a.a 1 3.b odd 2 1
2475.2.c.a 2 15.e even 4 2
2816.2.c.f 2 80.k odd 4 2
2816.2.c.j 2 80.q even 4 2
3025.2.a.a 1 11.b odd 2 1
3179.2.a.a 1 85.c even 2 1
3971.2.a.b 1 95.d odd 2 1
4400.2.a.i 1 4.b odd 2 1
4400.2.b.h 2 20.e even 4 2
4851.2.a.t 1 105.g even 2 1
5819.2.a.a 1 115.c odd 2 1
5929.2.a.h 1 385.h even 2 1
6336.2.a.br 1 120.i odd 2 1
6336.2.a.bu 1 120.m even 2 1
7744.2.a.k 1 440.c even 2 1
7744.2.a.x 1 440.o odd 2 1
8624.2.a.j 1 140.c even 2 1
9251.2.a.d 1 145.d even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(275))\).

Hecke characteristic polynomials

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