Properties

Label 33.2.a.a
Level 33
Weight 2
Character orbit 33.a
Self dual Yes
Analytic conductor 0.264
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 33 = 3 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 33.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.26350632667\)
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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} - q^{4} - 2q^{5} - q^{6} + 4q^{7} - 3q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} - q^{4} - 2q^{5} - q^{6} + 4q^{7} - 3q^{8} + q^{9} - 2q^{10} + q^{11} + q^{12} - 2q^{13} + 4q^{14} + 2q^{15} - q^{16} - 2q^{17} + q^{18} + 2q^{20} - 4q^{21} + q^{22} + 8q^{23} + 3q^{24} - q^{25} - 2q^{26} - q^{27} - 4q^{28} - 6q^{29} + 2q^{30} - 8q^{31} + 5q^{32} - q^{33} - 2q^{34} - 8q^{35} - q^{36} + 6q^{37} + 2q^{39} + 6q^{40} - 2q^{41} - 4q^{42} - q^{44} - 2q^{45} + 8q^{46} + 8q^{47} + q^{48} + 9q^{49} - q^{50} + 2q^{51} + 2q^{52} + 6q^{53} - q^{54} - 2q^{55} - 12q^{56} - 6q^{58} - 4q^{59} - 2q^{60} + 6q^{61} - 8q^{62} + 4q^{63} + 7q^{64} + 4q^{65} - q^{66} - 4q^{67} + 2q^{68} - 8q^{69} - 8q^{70} - 3q^{72} - 14q^{73} + 6q^{74} + q^{75} + 4q^{77} + 2q^{78} - 4q^{79} + 2q^{80} + q^{81} - 2q^{82} + 12q^{83} + 4q^{84} + 4q^{85} + 6q^{87} - 3q^{88} - 6q^{89} - 2q^{90} - 8q^{91} - 8q^{92} + 8q^{93} + 8q^{94} - 5q^{96} + 2q^{97} + 9q^{98} + q^{99} + O(q^{100}) \)

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 −2.00000 −1.00000 4.00000 −3.00000 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.

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(11\) \(-1\)

Hecke kernels

There are no other newforms in \(S_{2}^{\mathrm{new}}(\Gamma_0(33))\).