Properties

Label 99.2.a.d
Level 99
Weight 2
Character orbit 99.a
Self dual Yes
Analytic conductor 0.791
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 99.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.790518980011\)
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

\(f(q)\) \(=\) \( q + 2q^{2} + 2q^{4} - q^{5} - 2q^{7} + O(q^{10}) \) \( q + 2q^{2} + 2q^{4} - q^{5} - 2q^{7} - 2q^{10} - q^{11} + 4q^{13} - 4q^{14} - 4q^{16} + 2q^{17} - 2q^{20} - 2q^{22} + q^{23} - 4q^{25} + 8q^{26} - 4q^{28} + 7q^{31} - 8q^{32} + 4q^{34} + 2q^{35} + 3q^{37} + 8q^{41} - 6q^{43} - 2q^{44} + 2q^{46} - 8q^{47} - 3q^{49} - 8q^{50} + 8q^{52} + 6q^{53} + q^{55} - 5q^{59} + 12q^{61} + 14q^{62} - 8q^{64} - 4q^{65} - 7q^{67} + 4q^{68} + 4q^{70} + 3q^{71} + 4q^{73} + 6q^{74} + 2q^{77} - 10q^{79} + 4q^{80} + 16q^{82} + 6q^{83} - 2q^{85} - 12q^{86} - 15q^{89} - 8q^{91} + 2q^{92} - 16q^{94} - 7q^{97} - 6q^{98} + O(q^{100}) \)

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 −1.00000 0 −2.00000 0 0 −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
\(3\) \(-1\)
\(11\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(99))\):

\( T_{2} - 2 \)
\( T_{5} + 1 \)