Properties

Label 15.4.b
Level 15
Weight 4
Character orbit b
Rep. character \(\chi_{15}(4,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 15.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(15, [\chi])\).

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

Trace form

\(4q \) \(\mathstrut -\mathstrut 18q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 36q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 18q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 36q^{9} \) \(\mathstrut +\mathstrut 14q^{10} \) \(\mathstrut -\mathstrut 84q^{11} \) \(\mathstrut +\mathstrut 228q^{14} \) \(\mathstrut +\mathstrut 54q^{15} \) \(\mathstrut +\mathstrut 50q^{16} \) \(\mathstrut -\mathstrut 112q^{19} \) \(\mathstrut -\mathstrut 396q^{20} \) \(\mathstrut +\mathstrut 36q^{21} \) \(\mathstrut -\mathstrut 306q^{24} \) \(\mathstrut +\mathstrut 256q^{25} \) \(\mathstrut -\mathstrut 12q^{26} \) \(\mathstrut +\mathstrut 636q^{29} \) \(\mathstrut +\mathstrut 396q^{30} \) \(\mathstrut +\mathstrut 104q^{31} \) \(\mathstrut -\mathstrut 716q^{34} \) \(\mathstrut -\mathstrut 300q^{35} \) \(\mathstrut +\mathstrut 162q^{36} \) \(\mathstrut -\mathstrut 468q^{39} \) \(\mathstrut +\mathstrut 418q^{40} \) \(\mathstrut -\mathstrut 816q^{41} \) \(\mathstrut +\mathstrut 1116q^{44} \) \(\mathstrut -\mathstrut 54q^{45} \) \(\mathstrut +\mathstrut 184q^{46} \) \(\mathstrut -\mathstrut 140q^{49} \) \(\mathstrut -\mathstrut 696q^{50} \) \(\mathstrut +\mathstrut 612q^{51} \) \(\mathstrut -\mathstrut 162q^{54} \) \(\mathstrut -\mathstrut 864q^{55} \) \(\mathstrut +\mathstrut 60q^{56} \) \(\mathstrut +\mathstrut 372q^{59} \) \(\mathstrut +\mathstrut 126q^{60} \) \(\mathstrut +\mathstrut 680q^{61} \) \(\mathstrut +\mathstrut 958q^{64} \) \(\mathstrut +\mathstrut 948q^{65} \) \(\mathstrut -\mathstrut 1116q^{66} \) \(\mathstrut +\mathstrut 288q^{69} \) \(\mathstrut +\mathstrut 1080q^{70} \) \(\mathstrut -\mathstrut 72q^{71} \) \(\mathstrut -\mathstrut 3132q^{74} \) \(\mathstrut -\mathstrut 576q^{75} \) \(\mathstrut -\mathstrut 2448q^{76} \) \(\mathstrut -\mathstrut 760q^{79} \) \(\mathstrut +\mathstrut 444q^{80} \) \(\mathstrut +\mathstrut 324q^{81} \) \(\mathstrut +\mathstrut 2052q^{84} \) \(\mathstrut -\mathstrut 508q^{85} \) \(\mathstrut +\mathstrut 4296q^{86} \) \(\mathstrut -\mathstrut 2232q^{89} \) \(\mathstrut -\mathstrut 126q^{90} \) \(\mathstrut +\mathstrut 1944q^{91} \) \(\mathstrut +\mathstrut 3232q^{94} \) \(\mathstrut +\mathstrut 2784q^{95} \) \(\mathstrut -\mathstrut 1854q^{96} \) \(\mathstrut +\mathstrut 756q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(15, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
15.4.b.a \(4\) \(0.885\) \(\Q(i, \sqrt{41})\) None \(0\) \(0\) \(6\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-5+\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots\)