Properties

Label 2310.2.a.e
Level $2310$
Weight $2$
Character orbit 2310.a
Self dual yes
Analytic conductor $18.445$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2310.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(18.4454428669\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + q^{10} - q^{11} + q^{12} + q^{14} - q^{15} + q^{16} + 4 q^{17} - q^{18} - q^{20} - q^{21} + q^{22} + 2 q^{23} - q^{24} + q^{25} + q^{27} - q^{28} + 6 q^{29} + q^{30} - 8 q^{31} - q^{32} - q^{33} - 4 q^{34} + q^{35} + q^{36} - 8 q^{37} + q^{40} + 2 q^{41} + q^{42} - 4 q^{43} - q^{44} - q^{45} - 2 q^{46} + 12 q^{47} + q^{48} + q^{49} - q^{50} + 4 q^{51} + 14 q^{53} - q^{54} + q^{55} + q^{56} - 6 q^{58} - q^{60} + 10 q^{61} + 8 q^{62} - q^{63} + q^{64} + q^{66} + 2 q^{67} + 4 q^{68} + 2 q^{69} - q^{70} - 8 q^{71} - q^{72} + 6 q^{73} + 8 q^{74} + q^{75} + q^{77} + 8 q^{79} - q^{80} + q^{81} - 2 q^{82} - 8 q^{83} - q^{84} - 4 q^{85} + 4 q^{86} + 6 q^{87} + q^{88} - 12 q^{89} + q^{90} + 2 q^{92} - 8 q^{93} - 12 q^{94} - q^{96} + 6 q^{97} - q^{98} - q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)
\(5\) \(1\)
\(7\) \(1\)
\(11\) \(1\)

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 2310.2.a.e 1
3.b odd 2 1 6930.2.a.be 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2310.2.a.e 1 1.a even 1 1 trivial
6930.2.a.be 1 3.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2310))\):

\( T_{13} \)
\( T_{17} - 4 \)
\( T_{19} \)
\( T_{23} - 2 \)
\( T_{29} - 6 \)
\( T_{31} + 8 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( -1 + T \)
$5$ \( 1 + T \)
$7$ \( 1 + T \)
$11$ \( 1 + T \)
$13$ \( T \)
$17$ \( -4 + T \)
$19$ \( T \)
$23$ \( -2 + T \)
$29$ \( -6 + T \)
$31$ \( 8 + T \)
$37$ \( 8 + T \)
$41$ \( -2 + T \)
$43$ \( 4 + T \)
$47$ \( -12 + T \)
$53$ \( -14 + T \)
$59$ \( T \)
$61$ \( -10 + T \)
$67$ \( -2 + T \)
$71$ \( 8 + T \)
$73$ \( -6 + T \)
$79$ \( -8 + T \)
$83$ \( 8 + T \)
$89$ \( 12 + T \)
$97$ \( -6 + T \)
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