Properties

Label 20.4.e
Level 20
Weight 4
Character orbit e
Rep. character \(\chi_{20}(3,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 14
Newforms 2
Sturm bound 12
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 20.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 20 \)
Character field: \(\Q(i)\)
Newforms: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(20, [\chi])\).

Total New Old
Modular forms 22 22 0
Cusp forms 14 14 0
Eisenstein series 8 8 0

Trace form

\( 14q - 2q^{2} - 4q^{5} + 8q^{6} - 44q^{8} + O(q^{10}) \) \( 14q - 2q^{2} - 4q^{5} + 8q^{6} - 44q^{8} - 74q^{10} - 80q^{12} + 42q^{13} + 184q^{16} - 134q^{17} + 306q^{18} + 316q^{20} - 144q^{21} + 360q^{22} + 106q^{25} - 460q^{26} - 880q^{28} - 1240q^{30} - 632q^{32} + 80q^{33} + 892q^{36} + 326q^{37} + 1600q^{38} + 1836q^{40} + 288q^{41} + 1160q^{42} + 586q^{45} - 1432q^{46} - 2720q^{48} - 2214q^{50} - 1524q^{52} - 698q^{53} + 2048q^{56} - 960q^{57} + 2712q^{58} + 3280q^{60} - 1832q^{61} + 2440q^{62} - 1778q^{65} - 1680q^{66} - 2428q^{68} - 3040q^{70} - 2172q^{72} + 1942q^{73} + 800q^{76} + 3120q^{77} + 3720q^{78} + 2096q^{80} + 4530q^{81} + 536q^{82} + 2282q^{85} - 2552q^{86} - 2400q^{88} - 2154q^{90} - 1840q^{92} - 3280q^{93} + 1088q^{96} - 5994q^{97} + 326q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(20, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
20.4.e.a \(2\) \(1.180\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(4\) \(0\) \(-4\) \(0\) \(q+(2+2i)q^{2}+8iq^{4}+(-2-11i)q^{5}+\cdots\)
20.4.e.b \(12\) \(1.180\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{5})q^{2}-\beta _{9}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)