# 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 $0$

# Related objects

## 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

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

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