# Properties

 Label 120.3.l Level $120$ Weight $3$ Character orbit 120.l Rep. character $\chi_{120}(41,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $1$ Sturm bound $72$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$120 = 2^{3} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 120.l (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$72$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(120, [\chi])$$.

Total New Old
Modular forms 56 8 48
Cusp forms 40 8 32
Eisenstein series 16 0 16

## Trace form

 $$8 q - 4 q^{3} + 16 q^{7} + 20 q^{9} + O(q^{10})$$ $$8 q - 4 q^{3} + 16 q^{7} + 20 q^{9} - 8 q^{13} - 8 q^{19} + 28 q^{21} - 40 q^{25} + 20 q^{27} + 120 q^{31} - 112 q^{33} + 8 q^{37} - 72 q^{39} - 328 q^{43} - 60 q^{45} + 64 q^{49} + 64 q^{51} - 40 q^{55} + 72 q^{57} + 8 q^{61} + 88 q^{63} + 152 q^{67} + 100 q^{69} + 32 q^{73} + 20 q^{75} + 88 q^{79} + 224 q^{81} - 152 q^{87} + 560 q^{91} - 368 q^{93} + 144 q^{97} + 32 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(120, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
120.3.l.a $8$ $3.270$ 8.0.$$\cdots$$.5 None $$0$$ $$-4$$ $$0$$ $$16$$ $$q+\beta _{2}q^{3}+\beta _{6}q^{5}+(1+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(120, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(120, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 2}$$