Properties

Label 13.3.d
Level 13
Weight 3
Character orbit d
Rep. character \(\chi_{13}(5,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 4
Newforms 1
Sturm bound 3
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 13.d (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 13 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(13, [\chi])\).

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

Trace form

\(4q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 36q^{8} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 36q^{8} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 28q^{15} \) \(\mathstrut -\mathstrut 84q^{16} \) \(\mathstrut +\mathstrut 32q^{18} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut +\mathstrut 32q^{21} \) \(\mathstrut +\mathstrut 88q^{22} \) \(\mathstrut +\mathstrut 24q^{24} \) \(\mathstrut -\mathstrut 88q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 40q^{29} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 20q^{32} \) \(\mathstrut -\mathstrut 76q^{33} \) \(\mathstrut -\mathstrut 108q^{34} \) \(\mathstrut -\mathstrut 68q^{35} \) \(\mathstrut +\mathstrut 40q^{37} \) \(\mathstrut +\mathstrut 92q^{39} \) \(\mathstrut +\mathstrut 84q^{40} \) \(\mathstrut +\mathstrut 32q^{41} \) \(\mathstrut +\mathstrut 76q^{42} \) \(\mathstrut -\mathstrut 172q^{44} \) \(\mathstrut +\mathstrut 56q^{45} \) \(\mathstrut +\mathstrut 132q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 76q^{48} \) \(\mathstrut -\mathstrut 128q^{50} \) \(\mathstrut +\mathstrut 80q^{52} \) \(\mathstrut -\mathstrut 80q^{53} \) \(\mathstrut +\mathstrut 152q^{54} \) \(\mathstrut +\mathstrut 64q^{55} \) \(\mathstrut -\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 140q^{58} \) \(\mathstrut +\mathstrut 56q^{59} \) \(\mathstrut -\mathstrut 116q^{60} \) \(\mathstrut -\mathstrut 296q^{61} \) \(\mathstrut -\mathstrut 64q^{63} \) \(\mathstrut +\mathstrut 56q^{65} \) \(\mathstrut +\mathstrut 112q^{66} \) \(\mathstrut -\mathstrut 84q^{67} \) \(\mathstrut +\mathstrut 444q^{68} \) \(\mathstrut -\mathstrut 32q^{70} \) \(\mathstrut +\mathstrut 284q^{71} \) \(\mathstrut -\mathstrut 48q^{72} \) \(\mathstrut +\mathstrut 100q^{74} \) \(\mathstrut +\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 232q^{78} \) \(\mathstrut +\mathstrut 64q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut -\mathstrut 220q^{81} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 184q^{84} \) \(\mathstrut -\mathstrut 144q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 160q^{87} \) \(\mathstrut +\mathstrut 200q^{89} \) \(\mathstrut +\mathstrut 156q^{91} \) \(\mathstrut -\mathstrut 456q^{92} \) \(\mathstrut +\mathstrut 80q^{93} \) \(\mathstrut -\mathstrut 452q^{94} \) \(\mathstrut +\mathstrut 320q^{96} \) \(\mathstrut -\mathstrut 68q^{97} \) \(\mathstrut +\mathstrut 224q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(13, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
13.3.d.a \(4\) \(0.354\) \(\Q(i, \sqrt{10})\) None \(-4\) \(-4\) \(8\) \(-12\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots\)