# Properties

 Label 1368.3.o Level $1368$ Weight $3$ Character orbit 1368.o Rep. character $\chi_{1368}(721,\cdot)$ Character field $\Q$ Dimension $50$ Newform subspaces $4$ Sturm bound $720$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1368 = 2^{3} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1368.o (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$720$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(1368, [\chi])$$.

Total New Old
Modular forms 496 50 446
Cusp forms 464 50 414
Eisenstein series 32 0 32

## Trace form

 $$50 q - 16 q^{7} + O(q^{10})$$ $$50 q - 16 q^{7} + 4 q^{11} + 20 q^{17} + 10 q^{19} - 80 q^{23} + 218 q^{25} + 104 q^{35} - 44 q^{43} - 60 q^{47} + 302 q^{49} + 24 q^{55} - 32 q^{61} - 76 q^{73} - 236 q^{77} - 148 q^{83} - 244 q^{85} + 364 q^{95} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(1368, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1368.3.o.a $2$ $37.275$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$-14$$ $$22$$ $$q-7q^{5}+11q^{7}-3q^{11}+2\beta q^{13}+\cdots$$
1368.3.o.b $8$ $37.275$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$14$$ $$-6$$ $$q+(2+\beta _{4})q^{5}+(-1+\beta _{3})q^{7}+(4+\beta _{4}+\cdots)q^{11}+\cdots$$
1368.3.o.c $20$ $37.275$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-16$$ $$q-\beta _{4}q^{5}+(-1-\beta _{3})q^{7}+(-1-\beta _{1}+\cdots)q^{11}+\cdots$$
1368.3.o.d $20$ $37.275$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-16$$ $$q-\beta _{10}q^{5}+(-1+\beta _{3})q^{7}+\beta _{14}q^{11}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(1368, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(1368, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(152, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(342, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(456, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(684, [\chi])$$$$^{\oplus 2}$$