Properties

Label 2300.2.a.h
Level $2300$
Weight $2$
Character orbit 2300.a
Self dual yes
Analytic conductor $18.366$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2300.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(18.3655924649\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 92)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 3q^{3} + 4q^{7} + 6q^{9} + O(q^{10}) \) \( q + 3q^{3} + 4q^{7} + 6q^{9} + 2q^{11} + 5q^{13} - 4q^{17} - 2q^{19} + 12q^{21} - q^{23} + 9q^{27} - 7q^{29} - 3q^{31} + 6q^{33} - 2q^{37} + 15q^{39} - 9q^{41} + 8q^{43} - 9q^{47} + 9q^{49} - 12q^{51} - 2q^{53} - 6q^{57} - 2q^{61} + 24q^{63} - 14q^{67} - 3q^{69} - 3q^{71} + 3q^{73} + 8q^{77} - 6q^{79} + 9q^{81} - 8q^{83} - 21q^{87} + 12q^{89} + 20q^{91} - 9q^{93} + 12q^{99} + O(q^{100}) \)

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
0 3.00000 0 0 0 4.00000 0 6.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(1\)
\(23\) \(1\)

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 2300.2.a.h 1
4.b odd 2 1 9200.2.a.b 1
5.b even 2 1 92.2.a.a 1
5.c odd 4 2 2300.2.c.b 2
15.d odd 2 1 828.2.a.c 1
20.d odd 2 1 368.2.a.g 1
35.c odd 2 1 4508.2.a.d 1
40.e odd 2 1 1472.2.a.b 1
40.f even 2 1 1472.2.a.n 1
60.h even 2 1 3312.2.a.q 1
115.c odd 2 1 2116.2.a.a 1
460.g even 2 1 8464.2.a.s 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
92.2.a.a 1 5.b even 2 1
368.2.a.g 1 20.d odd 2 1
828.2.a.c 1 15.d odd 2 1
1472.2.a.b 1 40.e odd 2 1
1472.2.a.n 1 40.f even 2 1
2116.2.a.a 1 115.c odd 2 1
2300.2.a.h 1 1.a even 1 1 trivial
2300.2.c.b 2 5.c odd 4 2
3312.2.a.q 1 60.h even 2 1
4508.2.a.d 1 35.c odd 2 1
8464.2.a.s 1 460.g even 2 1
9200.2.a.b 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2300))\):

\( T_{3} - 3 \)
\( T_{7} - 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -3 + T \)
$5$ \( T \)
$7$ \( -4 + T \)
$11$ \( -2 + T \)
$13$ \( -5 + T \)
$17$ \( 4 + T \)
$19$ \( 2 + T \)
$23$ \( 1 + T \)
$29$ \( 7 + T \)
$31$ \( 3 + T \)
$37$ \( 2 + T \)
$41$ \( 9 + T \)
$43$ \( -8 + T \)
$47$ \( 9 + T \)
$53$ \( 2 + T \)
$59$ \( T \)
$61$ \( 2 + T \)
$67$ \( 14 + T \)
$71$ \( 3 + T \)
$73$ \( -3 + T \)
$79$ \( 6 + T \)
$83$ \( 8 + T \)
$89$ \( -12 + T \)
$97$ \( T \)
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