Properties

Label 4033.2.a.b
Level 4033
Weight 2
Character orbit 4033.a
Self dual Yes
Analytic conductor 32.204
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{4} - 2q^{5} + 2q^{7} - 3q^{8} - 3q^{9} + O(q^{10}) \) \( q + q^{2} - q^{4} - 2q^{5} + 2q^{7} - 3q^{8} - 3q^{9} - 2q^{10} + q^{11} - 5q^{13} + 2q^{14} - q^{16} - 3q^{17} - 3q^{18} + 2q^{20} + q^{22} + 2q^{23} - q^{25} - 5q^{26} - 2q^{28} - 4q^{31} + 5q^{32} - 3q^{34} - 4q^{35} + 3q^{36} - q^{37} + 6q^{40} + 12q^{41} + 11q^{43} - q^{44} + 6q^{45} + 2q^{46} + 9q^{47} - 3q^{49} - q^{50} + 5q^{52} - 8q^{53} - 2q^{55} - 6q^{56} + 2q^{59} + 10q^{61} - 4q^{62} - 6q^{63} + 7q^{64} + 10q^{65} + 8q^{67} + 3q^{68} - 4q^{70} - 6q^{71} + 9q^{72} - 10q^{73} - q^{74} + 2q^{77} - 2q^{79} + 2q^{80} + 9q^{81} + 12q^{82} - 12q^{83} + 6q^{85} + 11q^{86} - 3q^{88} - 14q^{89} + 6q^{90} - 10q^{91} - 2q^{92} + 9q^{94} + 16q^{97} - 3q^{98} - 3q^{99} + O(q^{100}) \)

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

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

\( p \) Sign
\(37\) \(1\)
\(109\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4033))\).