Properties

Label 15.4.b
Level $15$
Weight $4$
Character orbit 15.b
Rep. character $\chi_{15}(4,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{4}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

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