# Properties

 Label 1368.2.f Level $1368$ Weight $2$ Character orbit 1368.f Rep. character $\chi_{1368}(1025,\cdot)$ Character field $\Q$ Dimension $20$ Newform subspaces $4$ Sturm bound $480$ Trace bound $29$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1368 = 2^{3} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1368.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$480$$ Trace bound: $$29$$ Distinguishing $$T_p$$: $$5$$, $$29$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1368, [\chi])$$.

Total New Old
Modular forms 256 20 236
Cusp forms 224 20 204
Eisenstein series 32 0 32

## Trace form

 $$20 q + 8 q^{7} + O(q^{10})$$ $$20 q + 8 q^{7} + 4 q^{19} - 4 q^{25} - 8 q^{43} - 4 q^{49} + 48 q^{55} + 16 q^{61} + 32 q^{73} + 32 q^{85} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1368, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1368.2.f.a $2$ $10.924$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta q^{5}+2q^{7}-3\beta q^{11}-2\beta q^{13}+\cdots$$
1368.2.f.b $2$ $10.924$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta q^{5}+2q^{7}-3\beta q^{11}+2\beta q^{13}+\cdots$$
1368.2.f.c $8$ $10.924$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{7}q^{5}+\beta _{4}q^{7}+(\beta _{3}+\beta _{5})q^{11}+(\beta _{2}+\cdots)q^{13}+\cdots$$
1368.2.f.d $8$ $10.924$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{7}q^{5}+\beta _{4}q^{7}+(\beta _{3}+\beta _{5})q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1368, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1368, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(342, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(456, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(684, [\chi])$$$$^{\oplus 2}$$