# Properties

 Label 912.3.o Level $912$ Weight $3$ Character orbit 912.o Rep. character $\chi_{912}(721,\cdot)$ Character field $\Q$ Dimension $40$ Newform subspaces $5$ Sturm bound $480$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 912.o (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$480$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(912, [\chi])$$.

Total New Old
Modular forms 332 40 292
Cusp forms 308 40 268
Eisenstein series 24 0 24

## Trace form

 $$40 q + 16 q^{7} - 120 q^{9} + O(q^{10})$$ $$40 q + 16 q^{7} - 120 q^{9} - 32 q^{19} - 48 q^{23} + 200 q^{25} + 192 q^{35} - 48 q^{39} + 32 q^{43} + 192 q^{47} + 200 q^{49} + 240 q^{55} + 24 q^{57} + 128 q^{61} - 48 q^{63} - 80 q^{73} + 160 q^{77} + 360 q^{81} - 160 q^{83} + 192 q^{85} + 288 q^{87} + 96 q^{93} + 64 q^{95} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(912, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
912.3.o.a $2$ $24.850$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$8$$ $$20$$ $$q-\zeta_{6}q^{3}+4q^{5}+10q^{7}-3q^{9}-10q^{11}+\cdots$$
912.3.o.b $4$ $24.850$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$0$$ $$-10$$ $$-34$$ $$q-\beta _{1}q^{3}+(-2-\beta _{2})q^{5}+(-8-\beta _{2}+\cdots)q^{7}+\cdots$$
912.3.o.c $6$ $24.850$ 6.0.219615408.1 None $$0$$ $$0$$ $$-2$$ $$2$$ $$q+\beta _{2}q^{3}-\beta _{3}q^{5}-\beta _{1}q^{7}-3q^{9}+(4+\cdots)q^{11}+\cdots$$
912.3.o.d $8$ $24.850$ 8.0.$$\cdots$$.3 None $$0$$ $$0$$ $$4$$ $$12$$ $$q+\beta _{2}q^{3}+(1+\beta _{1}-\beta _{4})q^{5}+(1+\beta _{4}+\cdots)q^{7}+\cdots$$
912.3.o.e $20$ $24.850$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$16$$ $$q+\beta _{7}q^{3}-\beta _{4}q^{5}+(1+\beta _{3})q^{7}-3q^{9}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(912, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(912, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(152, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(304, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(456, [\chi])$$$$^{\oplus 2}$$