Properties

Label 2275.2.a.h
Level $2275$
Weight $2$
Character orbit 2275.a
Self dual yes
Analytic conductor $18.166$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2275 = 5^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2275.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(18.1659664598\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{2} + 2q^{4} + q^{7} - 3q^{9} + O(q^{10}) \) \( q + 2q^{2} + 2q^{4} + q^{7} - 3q^{9} - 6q^{11} + q^{13} + 2q^{14} - 4q^{16} - 4q^{17} - 6q^{18} + 5q^{19} - 12q^{22} - 3q^{23} + 2q^{26} + 2q^{28} - 5q^{29} - 3q^{31} - 8q^{32} - 8q^{34} - 6q^{36} + 4q^{37} + 10q^{38} - 6q^{41} + q^{43} - 12q^{44} - 6q^{46} - 7q^{47} + q^{49} + 2q^{52} + 9q^{53} - 10q^{58} + 8q^{59} - 10q^{61} - 6q^{62} - 3q^{63} - 8q^{64} + 6q^{67} - 8q^{68} - 8q^{71} + 13q^{73} + 8q^{74} + 10q^{76} - 6q^{77} + 3q^{79} + 9q^{81} - 12q^{82} - 15q^{83} + 2q^{86} + 3q^{89} + q^{91} - 6q^{92} - 14q^{94} - 7q^{97} + 2q^{98} + 18q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(7\) \(-1\)
\(13\) \(-1\)

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 2275.2.a.h 1
5.b even 2 1 91.2.a.a 1
15.d odd 2 1 819.2.a.f 1
20.d odd 2 1 1456.2.a.g 1
35.c odd 2 1 637.2.a.a 1
35.i odd 6 2 637.2.e.d 2
35.j even 6 2 637.2.e.e 2
40.e odd 2 1 5824.2.a.t 1
40.f even 2 1 5824.2.a.s 1
65.d even 2 1 1183.2.a.b 1
65.g odd 4 2 1183.2.c.b 2
105.g even 2 1 5733.2.a.l 1
455.h odd 2 1 8281.2.a.l 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
91.2.a.a 1 5.b even 2 1
637.2.a.a 1 35.c odd 2 1
637.2.e.d 2 35.i odd 6 2
637.2.e.e 2 35.j even 6 2
819.2.a.f 1 15.d odd 2 1
1183.2.a.b 1 65.d even 2 1
1183.2.c.b 2 65.g odd 4 2
1456.2.a.g 1 20.d odd 2 1
2275.2.a.h 1 1.a even 1 1 trivial
5733.2.a.l 1 105.g even 2 1
5824.2.a.s 1 40.f even 2 1
5824.2.a.t 1 40.e odd 2 1
8281.2.a.l 1 455.h odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2275))\):

\( T_{2} - 2 \)
\( T_{3} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -2 + T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( -1 + T \)
$11$ \( 6 + T \)
$13$ \( -1 + T \)
$17$ \( 4 + T \)
$19$ \( -5 + T \)
$23$ \( 3 + T \)
$29$ \( 5 + T \)
$31$ \( 3 + T \)
$37$ \( -4 + T \)
$41$ \( 6 + T \)
$43$ \( -1 + T \)
$47$ \( 7 + T \)
$53$ \( -9 + T \)
$59$ \( -8 + T \)
$61$ \( 10 + T \)
$67$ \( -6 + T \)
$71$ \( 8 + T \)
$73$ \( -13 + T \)
$79$ \( -3 + T \)
$83$ \( 15 + T \)
$89$ \( -3 + T \)
$97$ \( 7 + T \)
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