# Properties

 Label 1575.3.f Level $1575$ Weight $3$ Character orbit 1575.f Rep. character $\chi_{1575}(449,\cdot)$ Character field $\Q$ Dimension $72$ Newform subspaces $3$ Sturm bound $720$ Trace bound $16$

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## Defining parameters

 Level: $$N$$ $$=$$ $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1575.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$720$$ Trace bound: $$16$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(1575, [\chi])$$.

Total New Old
Modular forms 504 72 432
Cusp forms 456 72 384
Eisenstein series 48 0 48

## Trace form

 $$72 q + 160 q^{4} + O(q^{10})$$ $$72 q + 160 q^{4} + 80 q^{16} + 208 q^{19} + 320 q^{31} - 112 q^{34} + 96 q^{46} - 504 q^{49} + 208 q^{61} - 192 q^{64} + 1216 q^{76} + 224 q^{79} + 912 q^{94} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(1575, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1575.3.f.a $8$ $42.916$ 8.0.157351936.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}-\beta _{4}q^{4}-\beta _{1}q^{7}+(2\beta _{5}+\beta _{7})q^{8}+\cdots$$
1575.3.f.b $32$ $42.916$ None $$0$$ $$0$$ $$0$$ $$0$$
1575.3.f.c $32$ $42.916$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{3}^{\mathrm{old}}(1575, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(1575, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 2}$$