# Properties

 Label 150.3.k Level $150$ Weight $3$ Character orbit 150.k Rep. character $\chi_{150}(13,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $80$ Newform subspaces $2$ Sturm bound $90$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$150 = 2 \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 150.k (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$25$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$2$$ Sturm bound: $$90$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

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

Total New Old
Modular forms 512 80 432
Cusp forms 448 80 368
Eisenstein series 64 0 64

## Trace form

 $$80 q - 4 q^{2} + 16 q^{7} + 8 q^{8} + O(q^{10})$$ $$80 q - 4 q^{2} + 16 q^{7} + 8 q^{8} - 4 q^{10} - 12 q^{13} + 24 q^{15} + 80 q^{16} + 236 q^{17} + 48 q^{18} + 200 q^{19} + 32 q^{20} + 96 q^{22} + 96 q^{23} - 92 q^{25} + 40 q^{26} - 112 q^{28} - 400 q^{29} - 192 q^{30} - 64 q^{32} - 312 q^{33} - 100 q^{34} - 328 q^{35} - 120 q^{36} + 228 q^{37} + 64 q^{38} - 8 q^{40} - 160 q^{41} - 48 q^{42} + 432 q^{43} + 12 q^{45} + 64 q^{47} - 92 q^{50} - 24 q^{52} - 460 q^{53} - 672 q^{55} - 48 q^{57} - 64 q^{58} - 800 q^{59} + 48 q^{60} + 240 q^{61} + 80 q^{62} + 48 q^{63} + 44 q^{65} + 576 q^{67} + 88 q^{68} + 352 q^{70} - 24 q^{72} + 268 q^{73} - 48 q^{75} + 128 q^{77} - 96 q^{78} - 400 q^{79} + 180 q^{81} - 672 q^{82} + 448 q^{83} - 688 q^{85} + 528 q^{87} - 32 q^{88} + 100 q^{89} + 12 q^{90} + 32 q^{92} + 336 q^{93} + 256 q^{95} - 92 q^{97} + 124 q^{98} + O(q^{100})$$

## 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.k.a $32$ $4.087$ None $$8$$ $$0$$ $$0$$ $$8$$
150.3.k.b $48$ $4.087$ None $$-12$$ $$0$$ $$0$$ $$8$$

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

$$S_{3}^{\mathrm{old}}(150, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$