Properties

Label 20.3.d
Level 20
Weight 3
Character orbit d
Rep. character \(\chi_{20}(19,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 3
Sturm bound 9
Trace bound 2

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 20.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 20 \)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(9\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(20, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\(4q \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut 16q^{10} \) \(\mathstrut +\mathstrut 16q^{14} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 64q^{24} \) \(\mathstrut +\mathstrut 36q^{25} \) \(\mathstrut -\mathstrut 96q^{26} \) \(\mathstrut +\mathstrut 40q^{29} \) \(\mathstrut +\mathstrut 80q^{30} \) \(\mathstrut +\mathstrut 64q^{34} \) \(\mathstrut +\mathstrut 128q^{36} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut +\mathstrut 88q^{41} \) \(\mathstrut -\mathstrut 124q^{45} \) \(\mathstrut -\mathstrut 176q^{46} \) \(\mathstrut -\mathstrut 164q^{49} \) \(\mathstrut +\mathstrut 96q^{50} \) \(\mathstrut +\mathstrut 32q^{54} \) \(\mathstrut +\mathstrut 64q^{56} \) \(\mathstrut -\mathstrut 72q^{61} \) \(\mathstrut +\mathstrut 192q^{65} \) \(\mathstrut +\mathstrut 352q^{69} \) \(\mathstrut -\mathstrut 80q^{70} \) \(\mathstrut -\mathstrut 96q^{74} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut -\mathstrut 128q^{84} \) \(\mathstrut -\mathstrut 128q^{85} \) \(\mathstrut +\mathstrut 304q^{86} \) \(\mathstrut -\mathstrut 440q^{89} \) \(\mathstrut -\mathstrut 144q^{90} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 256q^{96} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(20, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
20.3.d.a \(1\) \(0.545\) \(\Q\) \(\Q(\sqrt{-5}) \) \(-2\) \(4\) \(-5\) \(-4\) \(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.b \(1\) \(0.545\) \(\Q\) \(\Q(\sqrt{-5}) \) \(2\) \(-4\) \(-5\) \(4\) \(q+2q^{2}-4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.c \(2\) \(0.545\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(6\) \(0\) \(q+iq^{2}-4q^{4}+(3-2i)q^{5}-4iq^{8}+\cdots\)