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

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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

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

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 \(-6\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{5})q^{2}-\beta _{9}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)