# Properties

 Label 816.2.c Level $816$ Weight $2$ Character orbit 816.c Rep. character $\chi_{816}(577,\cdot)$ Character field $\Q$ Dimension $18$ Newform subspaces $6$ Sturm bound $288$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$816 = 2^{4} \cdot 3 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 816.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$288$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(816, [\chi])$$.

Total New Old
Modular forms 156 18 138
Cusp forms 132 18 114
Eisenstein series 24 0 24

## Trace form

 $$18q - 18q^{9} + O(q^{10})$$ $$18q - 18q^{9} + 4q^{13} + 4q^{15} + 2q^{17} - 20q^{19} - 14q^{25} - 24q^{35} - 12q^{43} - 24q^{47} - 18q^{49} + 4q^{51} + 12q^{53} + 20q^{55} + 56q^{59} + 24q^{67} + 16q^{69} - 16q^{77} + 18q^{81} - 16q^{85} - 20q^{89} - 16q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(816, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
816.2.c.a $$2$$ $$6.516$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+2iq^{5}+2iq^{7}-q^{9}-6q^{13}+\cdots$$
816.2.c.b $$2$$ $$6.516$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+3iq^{5}-2iq^{7}-q^{9}+5iq^{11}+\cdots$$
816.2.c.c $$2$$ $$6.516$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-4iq^{7}-q^{9}+4iq^{11}+2q^{13}+\cdots$$
816.2.c.d $$2$$ $$6.516$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+iq^{5}-2iq^{7}-q^{9}-3iq^{11}+\cdots$$
816.2.c.e $$4$$ $$6.516$$ $$\Q(i, \sqrt{33})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}-2\beta _{2}q^{7}-q^{9}+\cdots$$
816.2.c.f $$6$$ $$6.516$$ 6.0.399424.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(816, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(816, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(34, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(51, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(68, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(102, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(136, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(204, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(272, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(408, [\chi])$$$$^{\oplus 2}$$