Properties

 Label 150.3.f Level $150$ Weight $3$ Character orbit 150.f Rep. character $\chi_{150}(7,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $12$ Newform subspaces $3$ Sturm bound $90$ Trace bound $7$

Related objects

Defining parameters

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

Dimensions

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

Total New Old
Modular forms 144 12 132
Cusp forms 96 12 84
Eisenstein series 48 0 48

Trace form

 $$12 q - 4 q^{2} + 16 q^{7} + 8 q^{8} + O(q^{10})$$ $$12 q - 4 q^{2} + 16 q^{7} + 8 q^{8} + 32 q^{11} - 12 q^{13} - 48 q^{16} - 44 q^{17} - 12 q^{18} + 24 q^{21} + 16 q^{22} + 16 q^{23} - 168 q^{26} - 32 q^{28} - 120 q^{31} + 16 q^{32} + 48 q^{33} + 72 q^{36} + 108 q^{37} + 64 q^{38} + 416 q^{41} - 48 q^{42} - 48 q^{43} + 64 q^{46} - 96 q^{47} - 96 q^{51} - 24 q^{52} - 100 q^{53} - 128 q^{56} - 48 q^{57} - 64 q^{58} - 8 q^{61} + 80 q^{62} + 48 q^{63} + 192 q^{66} + 16 q^{67} + 88 q^{68} - 128 q^{71} - 24 q^{72} + 188 q^{73} + 176 q^{76} + 128 q^{77} - 96 q^{78} - 108 q^{81} - 32 q^{82} - 192 q^{83} - 192 q^{86} + 48 q^{87} - 32 q^{88} - 936 q^{91} + 32 q^{92} + 96 q^{93} - 132 q^{97} + 124 q^{98} + O(q^{100})$$

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.f.a $4$ $4.087$ $$\Q(i, \sqrt{6})$$ None $$-4$$ $$0$$ $$0$$ $$-24$$ $$q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots$$
150.3.f.b $4$ $4.087$ $$\Q(i, \sqrt{6})$$ None $$-4$$ $$0$$ $$0$$ $$16$$ $$q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots$$
150.3.f.c $4$ $4.087$ $$\Q(i, \sqrt{6})$$ None $$4$$ $$0$$ $$0$$ $$24$$ $$q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(150, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(10, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$