# Properties

 Label 2028.2.q Level $2028$ Weight $2$ Character orbit 2028.q Rep. character $\chi_{2028}(361,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $50$ Newform subspaces $10$ Sturm bound $728$ Trace bound $17$

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## Defining parameters

 Level: $$N$$ $$=$$ $$2028 = 2^{2} \cdot 3 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2028.q (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$10$$ Sturm bound: $$728$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$5$$, $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2028, [\chi])$$.

Total New Old
Modular forms 812 50 762
Cusp forms 644 50 594
Eisenstein series 168 0 168

## Trace form

 $$50q + q^{3} - 3q^{7} - 25q^{9} + O(q^{10})$$ $$50q + q^{3} - 3q^{7} - 25q^{9} - 18q^{11} - 6q^{15} + 6q^{17} + 18q^{19} - 2q^{23} - 26q^{25} - 2q^{27} + 4q^{29} + 6q^{33} + 18q^{35} - 6q^{37} + 6q^{41} - 15q^{43} + 14q^{49} + 16q^{51} + 36q^{53} + 4q^{55} - 6q^{59} - q^{61} + 3q^{63} - 21q^{67} - 14q^{69} - 6q^{71} - 15q^{75} - 28q^{77} - 22q^{79} - 25q^{81} + 54q^{85} - 18q^{87} - 12q^{89} - 15q^{93} + 4q^{95} - 39q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2028, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2028.2.q.a $$2$$ $$16.194$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$-6$$ $$q+(1-\zeta_{6})q^{3}+(1-2\zeta_{6})q^{5}+(-4+2\zeta_{6})q^{7}+\cdots$$
2028.2.q.b $$2$$ $$16.194$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+(-2+4\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots$$
2028.2.q.c $$2$$ $$16.194$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots$$
2028.2.q.d $$4$$ $$16.194$$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{7}+(-1+\zeta_{12}^{2}+\cdots)q^{9}+\cdots$$
2028.2.q.e $$4$$ $$16.194$$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{3}+\zeta_{12}^{3}q^{5}-2\zeta_{12}q^{7}+\cdots$$
2028.2.q.f $$4$$ $$16.194$$ $$\Q(\sqrt{-3}, \sqrt{-43})$$ None $$0$$ $$-2$$ $$0$$ $$3$$ $$q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$$
2028.2.q.g $$4$$ $$16.194$$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\zeta_{12}^{2}q^{3}+2\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\cdots$$
2028.2.q.h $$4$$ $$16.194$$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\zeta_{12}^{2}q^{3}+2\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\cdots$$
2028.2.q.i $$12$$ $$16.194$$ 12.0.$$\cdots$$.1 None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+(-1+\beta _{7})q^{3}+(-2\beta _{2}+\beta _{6}-\beta _{8}+\cdots)q^{5}+\cdots$$
2028.2.q.j $$12$$ $$16.194$$ 12.0.$$\cdots$$.1 None $$0$$ $$6$$ $$0$$ $$0$$ $$q+\beta _{7}q^{3}+(-\beta _{2}-\beta _{8}-\beta _{11})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2028, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2028, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(52, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(156, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(169, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(338, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(507, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(676, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1014, [\chi])$$$$^{\oplus 2}$$