Properties

Label 112.2.a.b
Level 112
Weight 2
Character orbit 112.a
Self dual Yes
Analytic conductor 0.894
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 112.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.894324502638\)
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

\(f(q)\) \(=\) \( q + 2q^{5} + q^{7} - 3q^{9} + O(q^{10}) \) \( q + 2q^{5} + q^{7} - 3q^{9} + 4q^{11} + 2q^{13} - 6q^{17} - 8q^{19} - q^{25} + 6q^{29} - 8q^{31} + 2q^{35} - 2q^{37} + 2q^{41} + 4q^{43} - 6q^{45} + 8q^{47} + q^{49} + 6q^{53} + 8q^{55} - 6q^{61} - 3q^{63} + 4q^{65} + 4q^{67} + 8q^{71} + 10q^{73} + 4q^{77} - 16q^{79} + 9q^{81} - 8q^{83} - 12q^{85} - 6q^{89} + 2q^{91} - 16q^{95} - 6q^{97} - 12q^{99} + O(q^{100}) \)

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
0 0 0 2.00000 0 1.00000 0 −3.00000 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
\(2\) \(1\)
\(7\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{3} \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(112))\).