Properties

 Label 475.2.g Level $475$ Weight $2$ Character orbit 475.g Rep. character $\chi_{475}(18,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $56$ Newform subspaces $4$ Sturm bound $100$ Trace bound $1$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$475 = 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 475.g (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$100$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(475, [\chi])$$.

Total New Old
Modular forms 112 64 48
Cusp forms 88 56 32
Eisenstein series 24 8 16

Trace form

 $$56 q + 8 q^{6} + 6 q^{7} + O(q^{10})$$ $$56 q + 8 q^{6} + 6 q^{7} + 8 q^{11} - 100 q^{16} - 6 q^{17} + 4 q^{23} - 56 q^{26} - 8 q^{28} + 92 q^{36} - 4 q^{38} - 2 q^{43} + 18 q^{47} + 88 q^{58} + 64 q^{61} - 8 q^{62} - 78 q^{63} - 272 q^{66} - 72 q^{68} - 6 q^{73} + 156 q^{76} + 62 q^{77} - 64 q^{81} - 88 q^{82} + 68 q^{83} - 88 q^{87} + 4 q^{92} + 96 q^{93} + 120 q^{96} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(475, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
475.2.g.a $4$ $3.793$ $$\Q(i, \sqrt{19})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$0$$ $$-6$$ $$q-2\beta _{1}q^{4}+(-2+2\beta _{1}+\beta _{3})q^{7}+3\beta _{1}q^{9}+\cdots$$
475.2.g.b $12$ $3.793$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$12$$ $$q-\beta _{7}q^{2}+\beta _{5}q^{3}+(-\beta _{6}-\beta _{8})q^{4}+\cdots$$
475.2.g.c $16$ $3.793$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ $$\Q(\sqrt{-95})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{9}q^{2}-\beta _{3}q^{3}+(-2\beta _{7}-\beta _{10})q^{4}+\cdots$$
475.2.g.d $24$ $3.793$ None $$0$$ $$0$$ $$0$$ $$0$$

Decomposition of $$S_{2}^{\mathrm{old}}(475, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(475, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 2}$$