# Properties

 Label 252.3.z Level $252$ Weight $3$ Character orbit 252.z Rep. character $\chi_{252}(73,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $14$ Newform subspaces $5$ Sturm bound $144$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 252.z (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$144$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(252, [\chi])$$.

Total New Old
Modular forms 216 14 202
Cusp forms 168 14 154
Eisenstein series 48 0 48

## Trace form

 $$14 q + 3 q^{5} + 4 q^{7} + O(q^{10})$$ $$14 q + 3 q^{5} + 4 q^{7} - 3 q^{11} - 3 q^{17} + 45 q^{19} - 21 q^{23} + 68 q^{25} + 108 q^{29} + 105 q^{31} + 99 q^{35} + 35 q^{37} - 136 q^{43} - 141 q^{47} - 100 q^{49} - 105 q^{53} - 231 q^{59} + 39 q^{61} - 90 q^{65} - 77 q^{67} + 456 q^{71} - 99 q^{73} + 147 q^{77} + 115 q^{79} - 522 q^{85} - 423 q^{89} - 318 q^{91} - 69 q^{95} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(252, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
252.3.z.a $2$ $6.867$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$-14$$ $$q+(-2+\zeta_{6})q^{5}-7q^{7}+(15-15\zeta_{6})q^{11}+\cdots$$
252.3.z.b $2$ $6.867$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$13$$ $$q+(-2+\zeta_{6})q^{5}+(5+3\zeta_{6})q^{7}+(-3+\cdots)q^{11}+\cdots$$
252.3.z.c $2$ $6.867$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-11$$ $$q+(-8+5\zeta_{6})q^{7}+(-15+30\zeta_{6})q^{13}+\cdots$$
252.3.z.d $4$ $6.867$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$14$$ $$q+\beta _{2}q^{5}+(7+7\beta _{1})q^{7}+(-2\beta _{2}+\beta _{3})q^{11}+\cdots$$
252.3.z.e $4$ $6.867$ $$\Q(\sqrt{-3}, \sqrt{65})$$ None $$0$$ $$0$$ $$9$$ $$2$$ $$q+(2+\beta _{1}-\beta _{3})q^{5}+(1-\beta _{2})q^{7}+(-8\beta _{1}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(252, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(252, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(14, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 2}$$