Properties

Label 100.2.a.a
Level 100
Weight 2
Character orbit 100.a
Self dual Yes
Analytic conductor 0.799
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 100.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.798504020213\)
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

\(f(q)\) \(=\) \( q + 2q^{3} - 2q^{7} + q^{9} + O(q^{10}) \) \( q + 2q^{3} - 2q^{7} + q^{9} - 2q^{13} + 6q^{17} - 4q^{19} - 4q^{21} - 6q^{23} - 4q^{27} + 6q^{29} - 4q^{31} - 2q^{37} - 4q^{39} + 6q^{41} + 10q^{43} + 6q^{47} - 3q^{49} + 12q^{51} + 6q^{53} - 8q^{57} + 12q^{59} + 2q^{61} - 2q^{63} - 2q^{67} - 12q^{69} - 12q^{71} - 2q^{73} + 8q^{79} - 11q^{81} - 6q^{83} + 12q^{87} - 6q^{89} + 4q^{91} - 8q^{93} - 2q^{97} + O(q^{100}) \)

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
0 2.00000 0 0 0 −2.00000 0 1.00000 0
\(n\): 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
\(2\) \(-1\)
\(5\) \(1\)

Hecke kernels

There are no other newforms in \(S_{2}^{\mathrm{new}}(\Gamma_0(100))\).