# Properties

 Label 525.3.f Level $525$ Weight $3$ Character orbit 525.f Rep. character $\chi_{525}(449,\cdot)$ Character field $\Q$ Dimension $72$ Newform subspaces $3$ Sturm bound $240$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 525.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$240$$ Trace bound: $$6$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 172 72 100
Cusp forms 148 72 76
Eisenstein series 24 0 24

## Trace form

 $$72 q + 136 q^{4} + 24 q^{9} + O(q^{10})$$ $$72 q + 136 q^{4} + 24 q^{9} + 392 q^{16} - 104 q^{19} - 28 q^{21} + 172 q^{24} - 40 q^{31} + 128 q^{34} - 132 q^{36} - 44 q^{39} + 288 q^{46} - 504 q^{49} - 160 q^{51} - 380 q^{54} - 464 q^{61} + 1488 q^{64} - 748 q^{66} - 468 q^{69} + 16 q^{76} - 136 q^{79} + 496 q^{81} - 224 q^{84} + 168 q^{91} - 936 q^{94} + 852 q^{96} + 656 q^{99} + O(q^{100})$$

## 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.f.a $8$ $14.305$ 8.0.4337012736.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(-\beta _{2}+\beta _{3}+\beta _{4})q^{3}+(3+\cdots)q^{4}+\cdots$$
525.3.f.b $32$ $14.305$ None $$0$$ $$0$$ $$0$$ $$0$$
525.3.f.c $32$ $14.305$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{3}^{\mathrm{old}}(525, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 2}$$