# Properties

 Label 2028.2.b Level $2028$ Weight $2$ Character orbit 2028.b Rep. character $\chi_{2028}(337,\cdot)$ Character field $\Q$ Dimension $24$ Newform subspaces $7$ Sturm bound $728$ Trace bound $17$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2028 = 2^{2} \cdot 3 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2028.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$728$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 406 24 382
Cusp forms 322 24 298
Eisenstein series 84 0 84

## Trace form

 $$24 q + 24 q^{9} + O(q^{10})$$ $$24 q + 24 q^{9} - 12 q^{17} + 20 q^{23} - 12 q^{25} + 8 q^{29} + 12 q^{35} + 4 q^{43} - 24 q^{49} + 20 q^{51} - 24 q^{53} - 4 q^{55} - 24 q^{61} + 20 q^{69} - 16 q^{75} - 56 q^{77} + 12 q^{79} + 24 q^{81} - 12 q^{87} - 52 q^{95} + O(q^{100})$$

## 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.b.a $2$ $16.194$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+2iq^{5}-iq^{7}+q^{9}-2iq^{11}+\cdots$$
2028.2.b.b $2$ $16.194$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}-\zeta_{6}q^{5}-2\zeta_{6}q^{7}+q^{9}+2\zeta_{6}q^{11}+\cdots$$
2028.2.b.c $2$ $16.194$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+2iq^{5}-iq^{7}+q^{9}-2iq^{11}+\cdots$$
2028.2.b.d $2$ $16.194$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+iq^{7}+q^{9}+6q^{17}-iq^{19}+\cdots$$
2028.2.b.e $4$ $16.194$ $$\Q(\sqrt{-3}, \sqrt{-43})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+q^{3}+(-\beta _{1}-\beta _{3})q^{5}+\beta _{3}q^{7}+q^{9}+\cdots$$
2028.2.b.f $6$ $16.194$ 6.0.153664.1 None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-q^{3}+(\beta _{3}+\beta _{5})q^{5}+(-2\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$$
2028.2.b.g $6$ $16.194$ 6.0.153664.1 None $$0$$ $$6$$ $$0$$ $$0$$ $$q+q^{3}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\beta _{3}-2\beta _{5})q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(2028, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(156, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(169, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(338, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(507, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(676, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1014, [\chi])$$$$^{\oplus 2}$$