# Properties

 Label 825.2.c Level $825$ Weight $2$ Character orbit 825.c Rep. character $\chi_{825}(199,\cdot)$ Character field $\Q$ Dimension $28$ Newform subspaces $7$ Sturm bound $240$ Trace bound $14$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$825 = 3 \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 825.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$240$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$2$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(825, [\chi])$$.

Total New Old
Modular forms 132 28 104
Cusp forms 108 28 80
Eisenstein series 24 0 24

## Trace form

 $$28 q - 32 q^{4} + 8 q^{6} - 28 q^{9} + O(q^{10})$$ $$28 q - 32 q^{4} + 8 q^{6} - 28 q^{9} + 8 q^{14} + 56 q^{16} - 12 q^{19} - 4 q^{21} - 24 q^{24} - 8 q^{26} + 32 q^{29} + 4 q^{31} + 40 q^{34} + 32 q^{36} + 4 q^{39} - 32 q^{41} - 16 q^{44} - 24 q^{46} - 24 q^{49} + 16 q^{51} - 8 q^{54} - 72 q^{56} - 32 q^{59} + 12 q^{61} - 40 q^{64} - 8 q^{66} - 16 q^{69} + 96 q^{71} - 40 q^{74} + 72 q^{76} - 16 q^{79} + 28 q^{81} + 48 q^{84} + 72 q^{86} + 56 q^{89} - 28 q^{91} - 8 q^{94} - 24 q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(825, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
825.2.c.a $2$ $6.588$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}-q^{6}+4iq^{7}+\cdots$$
825.2.c.b $2$ $6.588$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+2q^{4}-iq^{7}-q^{9}-q^{11}+\cdots$$
825.2.c.c $4$ $6.588$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{2}q^{2}+\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{3}q^{6}+\cdots$$
825.2.c.d $4$ $6.588$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots$$
825.2.c.e $4$ $6.588$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots$$
825.2.c.f $6$ $6.588$ 6.0.5161984.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}+\beta _{4})q^{2}-\beta _{3}q^{3}+(-3-\beta _{1}+\cdots)q^{4}+\cdots$$
825.2.c.g $6$ $6.588$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(825, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(825, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(165, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(275, [\chi])$$$$^{\oplus 2}$$