Properties

 Label 150.3.j Level $150$ Weight $3$ Character orbit 150.j Rep. character $\chi_{150}(11,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $80$ Newform subspaces $1$ Sturm bound $90$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$150 = 2 \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 150.j (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$75$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$1$$ Sturm bound: $$90$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(150, [\chi])$$.

Total New Old
Modular forms 256 80 176
Cusp forms 224 80 144
Eisenstein series 32 0 32

Trace form

 $$80 q - 4 q^{3} + 40 q^{4} - 8 q^{7} + 20 q^{9} + O(q^{10})$$ $$80 q - 4 q^{3} + 40 q^{4} - 8 q^{7} + 20 q^{9} - 12 q^{12} + 40 q^{13} - 60 q^{15} - 80 q^{16} - 32 q^{18} + 60 q^{19} + 60 q^{21} - 8 q^{22} - 180 q^{25} + 182 q^{27} - 24 q^{28} + 20 q^{30} - 180 q^{31} + 26 q^{33} - 120 q^{34} - 40 q^{36} + 128 q^{37} + 220 q^{39} + 128 q^{42} - 56 q^{43} - 100 q^{45} - 120 q^{46} + 24 q^{48} + 440 q^{49} - 20 q^{51} - 80 q^{52} - 120 q^{54} - 792 q^{57} - 100 q^{60} + 200 q^{61} - 574 q^{63} + 160 q^{64} - 160 q^{66} - 732 q^{67} - 220 q^{69} + 280 q^{70} + 64 q^{72} - 400 q^{73} + 590 q^{75} + 80 q^{76} - 260 q^{78} + 400 q^{79} + 140 q^{81} + 448 q^{82} + 180 q^{84} - 200 q^{85} + 310 q^{87} - 64 q^{88} + 440 q^{90} + 340 q^{91} + 348 q^{93} + 160 q^{94} - 276 q^{97} + 180 q^{99} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(150, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
150.3.j.a $80$ $4.087$ None $$0$$ $$-4$$ $$0$$ $$-8$$

Decomposition of $$S_{3}^{\mathrm{old}}(150, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(150, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$