# Properties

 Label 1764.2.t Level $1764$ Weight $2$ Character orbit 1764.t Rep. character $\chi_{1764}(521,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $28$ Newform subspaces $3$ Sturm bound $672$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1764.t (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$672$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1764, [\chi])$$.

Total New Old
Modular forms 768 28 740
Cusp forms 576 28 548
Eisenstein series 192 0 192

## Trace form

 $$28 q + O(q^{10})$$ $$28 q - 18 q^{19} - 6 q^{25} + 6 q^{31} + 10 q^{37} + 4 q^{43} + 12 q^{61} - 50 q^{67} - 54 q^{73} - 6 q^{79} + 48 q^{85} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1764, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1764.2.t.a $4$ $14.086$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{11}+(1-2\beta _{1}+\cdots)q^{13}+\cdots$$
1764.2.t.b $8$ $14.086$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{2}q^{5}+(-\zeta_{24}^{3}-\zeta_{24}^{7})q^{11}+\cdots$$
1764.2.t.c $16$ $14.086$ $$\Q(\zeta_{48})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{48}^{4}-\zeta_{48}^{15})q^{5}+(\zeta_{48}-\zeta_{48}^{5}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1764, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1764, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(294, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(441, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(588, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(882, [\chi])$$$$^{\oplus 2}$$