Properties

Label 105.2.a.a
Level 105
Weight 2
Character orbit 105.a
Self dual Yes
Analytic conductor 0.838
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.838429221223\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + q^{7} - 3q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + q^{7} - 3q^{8} + q^{9} + q^{10} - q^{12} - 6q^{13} + q^{14} + q^{15} - q^{16} + 2q^{17} + q^{18} - 8q^{19} - q^{20} + q^{21} + 8q^{23} - 3q^{24} + q^{25} - 6q^{26} + q^{27} - q^{28} - 2q^{29} + q^{30} + 4q^{31} + 5q^{32} + 2q^{34} + q^{35} - q^{36} - 2q^{37} - 8q^{38} - 6q^{39} - 3q^{40} - 6q^{41} + q^{42} + 4q^{43} + q^{45} + 8q^{46} + 8q^{47} - q^{48} + q^{49} + q^{50} + 2q^{51} + 6q^{52} + 10q^{53} + q^{54} - 3q^{56} - 8q^{57} - 2q^{58} + 4q^{59} - q^{60} - 2q^{61} + 4q^{62} + q^{63} + 7q^{64} - 6q^{65} + 4q^{67} - 2q^{68} + 8q^{69} + q^{70} - 12q^{71} - 3q^{72} - 2q^{73} - 2q^{74} + q^{75} + 8q^{76} - 6q^{78} + 8q^{79} - q^{80} + q^{81} - 6q^{82} - 4q^{83} - q^{84} + 2q^{85} + 4q^{86} - 2q^{87} - 6q^{89} + q^{90} - 6q^{91} - 8q^{92} + 4q^{93} + 8q^{94} - 8q^{95} + 5q^{96} - 18q^{97} + q^{98} + O(q^{100}) \)

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
1.00000 1.00000 −1.00000 1.00000 1.00000 1.00000 −3.00000 1.00000 1.00000
\(n\): 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
\(3\) \(-1\)
\(5\) \(-1\)
\(7\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(105))\).