# Properties

 Label 525.3.s Level $525$ Weight $3$ Character orbit 525.s Rep. character $\chi_{525}(124,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $96$ Newform subspaces $10$ Sturm bound $240$ Trace bound $14$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 525.s (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$10$$ Sturm bound: $$240$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$2$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(525, [\chi])$$.

Total New Old
Modular forms 344 96 248
Cusp forms 296 96 200
Eisenstein series 48 0 48

## Trace form

 $$96 q + 96 q^{4} - 144 q^{9} + O(q^{10})$$ $$96 q + 96 q^{4} - 144 q^{9} + 36 q^{11} - 60 q^{14} - 240 q^{16} + 150 q^{19} + 6 q^{21} + 192 q^{26} + 96 q^{29} - 48 q^{31} - 576 q^{36} + 18 q^{39} - 420 q^{44} + 120 q^{46} - 462 q^{49} - 24 q^{51} + 516 q^{56} + 1128 q^{59} - 102 q^{61} - 1440 q^{64} + 216 q^{66} - 528 q^{71} - 600 q^{74} + 120 q^{79} - 432 q^{81} - 600 q^{84} + 252 q^{86} - 48 q^{89} + 678 q^{91} + 1368 q^{94} - 900 q^{96} - 216 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(525, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
525.3.s.a $4$ $14.305$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}-3\zeta_{12}^{2}q^{4}+\cdots$$
525.3.s.b $4$ $14.305$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}-3\zeta_{12}^{2}q^{4}+\cdots$$
525.3.s.c $4$ $14.305$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}-3\zeta_{12}^{2}q^{4}+\cdots$$
525.3.s.d $4$ $14.305$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(-2+\cdots)q^{6}+\cdots$$
525.3.s.e $4$ $14.305$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+5\zeta_{12}^{2}q^{4}+\cdots$$
525.3.s.f $4$ $14.305$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+5\zeta_{12}^{2}q^{4}+\cdots$$
525.3.s.g $8$ $14.305$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(\zeta_{24}+\zeta_{24}^{3})q^{3}+\cdots$$
525.3.s.h $16$ $14.305$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{11}q^{2}+(-\beta _{10}+2\beta _{13})q^{3}+(1+\cdots)q^{4}+\cdots$$
525.3.s.i $24$ $14.305$ None $$0$$ $$0$$ $$0$$ $$0$$
525.3.s.j $24$ $14.305$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{3}^{\mathrm{old}}(525, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(525, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 2}$$