# Properties

 Label 1512.2.k Level $1512$ Weight $2$ Character orbit 1512.k Rep. character $\chi_{1512}(377,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $2$ Sturm bound $576$ Trace bound $25$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1512 = 2^{3} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1512.k (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$576$$ Trace bound: $$25$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1512, [\chi])$$.

Total New Old
Modular forms 312 32 280
Cusp forms 264 32 232
Eisenstein series 48 0 48

## Trace form

 $$32q - 4q^{7} + O(q^{10})$$ $$32q - 4q^{7} + 24q^{25} - 16q^{37} + 28q^{43} + 4q^{49} + 16q^{67} - 4q^{79} + 32q^{85} + 54q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1512, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1512.2.k.a $$16$$ $$12.073$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-\beta _{9}q^{5}-\beta _{1}q^{7}-\beta _{10}q^{11}-\beta _{5}q^{13}+\cdots$$
1512.2.k.b $$16$$ $$12.073$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+\beta _{1}q^{5}-\beta _{12}q^{7}+\beta _{10}q^{11}+(\beta _{4}+\cdots)q^{13}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1512, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1512, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(189, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(378, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(504, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(756, [\chi])$$$$^{\oplus 2}$$