# Properties

 Label 525.2.r Level $525$ Weight $2$ Character orbit 525.r Rep. character $\chi_{525}(424,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $48$ Newform subspaces $8$ Sturm bound $160$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 525.r (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$8$$ Sturm bound: $$160$$ Trace bound: $$6$$ Distinguishing $$T_p$$: $$2$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(525, [\chi])$$.

Total New Old
Modular forms 184 48 136
Cusp forms 136 48 88
Eisenstein series 48 0 48

## Trace form

 $$48 q + 24 q^{4} + 8 q^{6} + 24 q^{9} + O(q^{10})$$ $$48 q + 24 q^{4} + 8 q^{6} + 24 q^{9} - 4 q^{11} + 36 q^{14} - 40 q^{16} + 22 q^{19} - 2 q^{21} + 12 q^{24} + 24 q^{26} - 32 q^{29} - 32 q^{31} - 32 q^{34} + 48 q^{36} - 2 q^{39} - 8 q^{41} + 36 q^{44} - 8 q^{46} + 74 q^{49} - 8 q^{51} + 4 q^{54} - 108 q^{56} + 8 q^{59} - 2 q^{61} - 208 q^{64} - 40 q^{66} - 48 q^{69} + 80 q^{71} - 8 q^{74} - 8 q^{76} - 12 q^{79} - 24 q^{81} - 72 q^{84} + 12 q^{86} - 32 q^{89} + 58 q^{91} + 48 q^{94} - 8 q^{96} - 8 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(525, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
525.2.r.a $4$ $4.192$ $$\Q(\zeta_{12})$$ None $$-6$$ $$0$$ $$0$$ $$10$$ $$q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$$
525.2.r.b $4$ $4.192$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}+(-2+2\zeta_{12}^{2})q^{4}+(-\zeta_{12}+\cdots)q^{7}+\cdots$$
525.2.r.c $4$ $4.192$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$$
525.2.r.d $4$ $4.192$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots$$
525.2.r.e $4$ $4.192$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots$$
525.2.r.f $4$ $4.192$ $$\Q(\zeta_{12})$$ None $$6$$ $$0$$ $$0$$ $$-10$$ $$q+(2-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+\cdots$$
525.2.r.g $8$ $4.192$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{5}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{7}q^{6}+(\zeta_{24}+\cdots)q^{7}+\cdots$$
525.2.r.h $16$ $4.192$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(525, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(525, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 2}$$