Properties

Label 1502.2.a.a
Level 1502
Weight 2
Character orbit 1502.a
Self dual yes
Analytic conductor 11.994
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 1502 = 2 \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1502.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.9935303836\)
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

\(f(q)\) \(=\) \( q + q^{2} - 2q^{3} + q^{4} + 2q^{5} - 2q^{6} + 4q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - 2q^{3} + q^{4} + 2q^{5} - 2q^{6} + 4q^{7} + q^{8} + q^{9} + 2q^{10} + 2q^{11} - 2q^{12} - 2q^{13} + 4q^{14} - 4q^{15} + q^{16} + 6q^{17} + q^{18} + 2q^{20} - 8q^{21} + 2q^{22} - 2q^{24} - q^{25} - 2q^{26} + 4q^{27} + 4q^{28} - 4q^{30} - 4q^{31} + q^{32} - 4q^{33} + 6q^{34} + 8q^{35} + q^{36} - 2q^{37} + 4q^{39} + 2q^{40} - 2q^{41} - 8q^{42} - 4q^{43} + 2q^{44} + 2q^{45} - 8q^{47} - 2q^{48} + 9q^{49} - q^{50} - 12q^{51} - 2q^{52} + 6q^{53} + 4q^{54} + 4q^{55} + 4q^{56} + 12q^{59} - 4q^{60} + 6q^{61} - 4q^{62} + 4q^{63} + q^{64} - 4q^{65} - 4q^{66} + 2q^{67} + 6q^{68} + 8q^{70} + 8q^{71} + q^{72} - 14q^{73} - 2q^{74} + 2q^{75} + 8q^{77} + 4q^{78} + 12q^{79} + 2q^{80} - 11q^{81} - 2q^{82} + 6q^{83} - 8q^{84} + 12q^{85} - 4q^{86} + 2q^{88} - 2q^{89} + 2q^{90} - 8q^{91} + 8q^{93} - 8q^{94} - 2q^{96} + 10q^{97} + 9q^{98} + 2q^{99} + O(q^{100}) \)

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 2.00000 −2.00000 4.00000 1.00000 1.00000 2.00000
\(n\): 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 1502.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1502.2.a.a 1 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(751\) \(1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1502))\).