# Properties

 Label 2475.2.f Level $2475$ Weight $2$ Character orbit 2475.f Rep. character $\chi_{2475}(2276,\cdot)$ Character field $\Q$ Dimension $76$ Newform subspaces $9$ Sturm bound $720$ Trace bound $22$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2475 = 3^{2} \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2475.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$33$$ Character field: $$\Q$$ Newform subspaces: $$9$$ Sturm bound: $$720$$ Trace bound: $$22$$ Distinguishing $$T_p$$: $$2$$, $$29$$, $$37$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2475, [\chi])$$.

Total New Old
Modular forms 384 76 308
Cusp forms 336 76 260
Eisenstein series 48 0 48

## Trace form

 $$76 q + 76 q^{4} + O(q^{10})$$ $$76 q + 76 q^{4} + 84 q^{16} - 4 q^{22} + 32 q^{31} - 32 q^{34} - 68 q^{49} + 16 q^{58} + 92 q^{64} + 48 q^{67} - 112 q^{82} + 68 q^{88} - 16 q^{91} + 40 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2475, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2475.2.f.a $$2$$ $$19.763$$ $$\Q(\sqrt{-2})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}-q^{4}-\beta q^{7}+3q^{8}+(-3+\beta )q^{11}+\cdots$$
2475.2.f.b $$2$$ $$19.763$$ $$\Q(\sqrt{-2})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}-q^{4}-\beta q^{7}+3q^{8}+(3+\beta )q^{11}+\cdots$$
2475.2.f.c $$2$$ $$19.763$$ $$\Q(\sqrt{-2})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}-q^{4}-\beta q^{7}-3q^{8}+(-3-\beta )q^{11}+\cdots$$
2475.2.f.d $$2$$ $$19.763$$ $$\Q(\sqrt{-2})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}-q^{4}+\beta q^{7}-3q^{8}+(3+\beta )q^{11}+\cdots$$
2475.2.f.e $$4$$ $$19.763$$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+q^{4}-\beta _{3}q^{7}-\beta _{2}q^{8}+(2\beta _{1}+\cdots)q^{11}+\cdots$$
2475.2.f.f $$16$$ $$19.763$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{9}q^{2}+(1-\beta _{3})q^{4}+\beta _{5}q^{7}+(\beta _{9}+\cdots)q^{8}+\cdots$$
2475.2.f.g $$16$$ $$19.763$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{9}q^{2}+(1-\beta _{3})q^{4}+\beta _{5}q^{7}+(\beta _{9}+\cdots)q^{8}+\cdots$$
2475.2.f.h $$16$$ $$19.763$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(1+\beta _{1}+\beta _{5})q^{4}+(\beta _{3}-\beta _{8}+\cdots)q^{7}+\cdots$$
2475.2.f.i $$16$$ $$19.763$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ $$\Q(\sqrt{-55})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+(2-\beta _{1})q^{4}-\beta _{15}q^{7}+(\beta _{4}+\cdots)q^{8}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2475, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2475, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(99, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(165, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(495, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(825, [\chi])$$$$^{\oplus 2}$$