# Properties

 Label 920.2.e Level $920$ Weight $2$ Character orbit 920.e Rep. character $\chi_{920}(369,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $3$ Sturm bound $288$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$920 = 2^{3} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 920.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$288$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(920, [\chi])$$.

Total New Old
Modular forms 152 32 120
Cusp forms 136 32 104
Eisenstein series 16 0 16

## Trace form

 $$32 q + 4 q^{5} - 28 q^{9} + O(q^{10})$$ $$32 q + 4 q^{5} - 28 q^{9} + 4 q^{15} + 4 q^{25} - 4 q^{29} - 8 q^{31} + 12 q^{35} + 24 q^{39} - 16 q^{45} - 48 q^{49} - 24 q^{51} - 8 q^{55} - 60 q^{59} + 40 q^{61} - 20 q^{65} + 8 q^{69} - 24 q^{71} + 48 q^{75} + 72 q^{79} + 16 q^{81} - 12 q^{85} - 24 q^{89} - 48 q^{91} + 24 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(920, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
920.2.e.a $2$ $7.346$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+2iq^{3}+(2-i)q^{5}-3iq^{7}-q^{9}+\cdots$$
920.2.e.b $14$ $7.346$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{8}q^{3}+\beta _{3}q^{5}+(\beta _{7}-\beta _{13})q^{7}+(1+\cdots)q^{9}+\cdots$$
920.2.e.c $16$ $7.346$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta _{5}q^{3}-\beta _{7}q^{5}+(-\beta _{2}+\beta _{13})q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(920, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(920, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(115, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(230, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(460, [\chi])$$$$^{\oplus 2}$$