Properties

Label 20.3.d.a
Level 20
Weight 3
Character orbit 20.d
Self dual Yes
Analytic conductor 0.545
Analytic rank 0
Dimension 1
CM disc. -20
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 20.d (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(0.544960528721\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut 10q^{10} \) \(\mathstrut +\mathstrut 16q^{12} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut -\mathstrut 20q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 32q^{24} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 8q^{27} \) \(\mathstrut -\mathstrut 16q^{28} \) \(\mathstrut -\mathstrut 22q^{29} \) \(\mathstrut +\mathstrut 40q^{30} \) \(\mathstrut -\mathstrut 32q^{32} \) \(\mathstrut +\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 28q^{36} \) \(\mathstrut +\mathstrut 40q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 35q^{45} \) \(\mathstrut -\mathstrut 88q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut -\mathstrut 33q^{49} \) \(\mathstrut -\mathstrut 50q^{50} \) \(\mathstrut +\mathstrut 16q^{54} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 80q^{60} \) \(\mathstrut -\mathstrut 58q^{61} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 64q^{64} \) \(\mathstrut +\mathstrut 116q^{67} \) \(\mathstrut +\mathstrut 176q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 56q^{72} \) \(\mathstrut +\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 80q^{80} \) \(\mathstrut -\mathstrut 95q^{81} \) \(\mathstrut -\mathstrut 124q^{82} \) \(\mathstrut -\mathstrut 76q^{83} \) \(\mathstrut -\mathstrut 64q^{84} \) \(\mathstrut +\mathstrut 152q^{86} \) \(\mathstrut -\mathstrut 88q^{87} \) \(\mathstrut -\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 70q^{90} \) \(\mathstrut +\mathstrut 176q^{92} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 128q^{96} \) \(\mathstrut +\mathstrut 66q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(17\)
\(\chi(n)\) \(-1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
19.1
0
−2.00000 4.00000 4.00000 −5.00000 −8.00000 −4.00000 −8.00000 7.00000 10.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char. orbit Parity Mult. Self Twist Proved
1.a Even 1 trivial yes
20.d Odd 1 CM by \(\Q(\sqrt{-5}) \) yes

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3} \) \(\mathstrut -\mathstrut 4 \) acting on \(S_{3}^{\mathrm{new}}(20, [\chi])\).