Properties

 Label 120.2.f Level $120$ Weight $2$ Character orbit 120.f Rep. character $\chi_{120}(49,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $48$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$120 = 2^{3} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 120.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$48$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(120, [\chi])$$.

Total New Old
Modular forms 32 2 30
Cusp forms 16 2 14
Eisenstein series 16 0 16

Trace form

 $$2 q + 4 q^{5} - 2 q^{9} + O(q^{10})$$ $$2 q + 4 q^{5} - 2 q^{9} + 4 q^{11} + 2 q^{15} - 16 q^{19} - 4 q^{21} + 6 q^{25} - 16 q^{29} + 4 q^{35} - 4 q^{39} + 4 q^{41} - 4 q^{45} + 6 q^{49} + 12 q^{51} + 8 q^{55} + 12 q^{59} + 4 q^{61} + 4 q^{65} + 8 q^{69} - 8 q^{71} + 8 q^{75} + 16 q^{79} + 2 q^{81} - 12 q^{85} - 12 q^{89} - 8 q^{91} - 32 q^{95} - 4 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(120, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
120.2.f.a $2$ $0.958$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{3}+(2-i)q^{5}+2iq^{7}-q^{9}+2q^{11}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(120, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(120, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 2}$$