# Properties

 Label 150.3.d Level $150$ Weight $3$ Character orbit 150.d Rep. character $\chi_{150}(101,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $4$ Sturm bound $90$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$150 = 2 \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 150.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$90$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

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

Total New Old
Modular forms 72 12 60
Cusp forms 48 12 36
Eisenstein series 24 0 24

## Trace form

 $$12 q - 4 q^{3} - 24 q^{4} + 8 q^{6} - 8 q^{7} - 4 q^{9} + O(q^{10})$$ $$12 q - 4 q^{3} - 24 q^{4} + 8 q^{6} - 8 q^{7} - 4 q^{9} + 8 q^{12} + 40 q^{13} + 48 q^{16} - 32 q^{18} - 44 q^{19} + 44 q^{21} - 48 q^{22} - 16 q^{24} - 28 q^{27} + 16 q^{28} - 124 q^{31} - 24 q^{33} + 112 q^{34} + 8 q^{36} + 88 q^{37} + 60 q^{39} + 128 q^{42} - 56 q^{43} - 32 q^{46} - 16 q^{48} + 120 q^{49} - 184 q^{51} - 80 q^{52} - 40 q^{54} - 152 q^{57} - 132 q^{61} + 256 q^{63} - 96 q^{64} - 176 q^{66} + 328 q^{67} + 224 q^{69} + 64 q^{72} - 200 q^{73} + 88 q^{76} - 40 q^{78} - 56 q^{79} + 284 q^{81} - 192 q^{82} - 88 q^{84} - 240 q^{87} + 96 q^{88} + 620 q^{91} - 32 q^{93} + 80 q^{94} + 32 q^{96} - 296 q^{97} - 656 q^{99} + O(q^{100})$$

## 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.d.a $2$ $4.087$ $$\Q(\sqrt{-2})$$ None $$0$$ $$-2$$ $$0$$ $$-14$$ $$q+\beta q^{2}+(-1-2\beta )q^{3}-2q^{4}+(4-\beta )q^{6}+\cdots$$
150.3.d.b $2$ $4.087$ $$\Q(\sqrt{-2})$$ None $$0$$ $$2$$ $$0$$ $$14$$ $$q+\beta q^{2}+(1-2\beta )q^{3}-2q^{4}+(4+\beta )q^{6}+\cdots$$
150.3.d.c $4$ $4.087$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$-4$$ $$0$$ $$-8$$ $$q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}-2q^{4}+\cdots$$
150.3.d.d $4$ $4.087$ $$\Q(\sqrt{-2}, \sqrt{-17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-\beta _{1}q^{3}-2q^{4}+(-1+\beta _{3})q^{6}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(150, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$