# Properties

 Label 150.2.h Level $150$ Weight $2$ Character orbit 150.h Rep. character $\chi_{150}(19,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $24$ Newform subspaces $2$ Sturm bound $60$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$150 = 2 \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 150.h (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$25$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$2$$ Sturm bound: $$60$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(150, [\chi])$$.

Total New Old
Modular forms 136 24 112
Cusp forms 104 24 80
Eisenstein series 32 0 32

## Trace form

 $$24 q + 6 q^{4} + 4 q^{5} - 2 q^{6} + 6 q^{9} + O(q^{10})$$ $$24 q + 6 q^{4} + 4 q^{5} - 2 q^{6} + 6 q^{9} + 2 q^{10} + 12 q^{11} - 2 q^{15} - 6 q^{16} - 20 q^{17} - 8 q^{19} - 4 q^{20} - 4 q^{21} - 20 q^{22} - 20 q^{23} - 8 q^{24} + 14 q^{25} + 8 q^{26} - 10 q^{28} - 32 q^{29} - 16 q^{30} + 6 q^{31} - 20 q^{33} + 20 q^{34} - 24 q^{35} - 6 q^{36} - 2 q^{40} + 44 q^{41} + 10 q^{42} + 8 q^{44} - 4 q^{45} + 4 q^{46} - 40 q^{47} - 44 q^{49} - 8 q^{50} + 16 q^{51} + 2 q^{54} + 28 q^{55} + 12 q^{60} + 12 q^{61} + 60 q^{62} + 20 q^{63} + 6 q^{64} + 12 q^{65} - 8 q^{66} - 40 q^{67} + 16 q^{69} - 22 q^{70} - 8 q^{71} + 8 q^{74} + 8 q^{75} + 8 q^{76} + 80 q^{77} - 4 q^{79} + 4 q^{80} - 6 q^{81} + 40 q^{83} + 4 q^{84} + 16 q^{85} - 24 q^{86} - 20 q^{87} + 10 q^{88} + 36 q^{89} - 2 q^{90} - 12 q^{91} + 32 q^{94} - 2 q^{96} + 50 q^{97} + 80 q^{98} + 8 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(150, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
150.2.h.a $8$ $1.198$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{20}q^{2}-\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(\zeta_{20}+\cdots)q^{5}+\cdots$$
150.2.h.b $16$ $1.198$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+\beta _{8}q^{2}+\beta _{6}q^{3}-\beta _{10}q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(150, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(150, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$