# Properties

 Label 475.2.e Level $475$ Weight $2$ Character orbit 475.e Rep. character $\chi_{475}(26,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $56$ Newform subspaces $8$ Sturm bound $100$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$475 = 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 475.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$8$$ Sturm bound: $$100$$ Trace bound: $$2$$ 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 68 44
Cusp forms 88 56 32
Eisenstein series 24 12 12

## Trace form

 $$56 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 6 q^{6} + 12 q^{7} - 12 q^{8} - 22 q^{9} + O(q^{10})$$ $$56 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 6 q^{6} + 12 q^{7} - 12 q^{8} - 22 q^{9} - 12 q^{11} - 12 q^{12} - 6 q^{13} - 8 q^{16} + 6 q^{17} - 8 q^{18} - 16 q^{19} - 18 q^{21} - 6 q^{22} + 6 q^{23} - 26 q^{24} + 12 q^{26} - 16 q^{27} - 6 q^{29} + 4 q^{31} + 24 q^{32} + 24 q^{33} + 10 q^{34} + 6 q^{36} - 8 q^{37} + 6 q^{38} + 40 q^{39} - 22 q^{41} - 38 q^{42} - 4 q^{43} - 22 q^{44} - 16 q^{46} + 16 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 8 q^{54} + 56 q^{56} + 28 q^{57} + 68 q^{58} - 32 q^{59} - 30 q^{61} + 24 q^{62} + 2 q^{63} - 64 q^{64} - 72 q^{66} - 14 q^{67} - 76 q^{68} + 60 q^{69} - 24 q^{71} + 28 q^{72} - 34 q^{73} + 8 q^{74} + 20 q^{76} + 28 q^{77} + 12 q^{78} - 30 q^{79} - 16 q^{81} + 52 q^{82} - 20 q^{83} + 116 q^{84} + 14 q^{86} - 4 q^{87} + 32 q^{88} - 20 q^{89} + 42 q^{91} + 40 q^{92} + 12 q^{93} + 120 q^{94} + 76 q^{96} + 16 q^{97} + 32 q^{98} + 36 q^{99} + O(q^{100})$$

## 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.e.a $2$ $3.793$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$0$$ $$-8$$ $$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-4q^{7}+\cdots$$
475.2.e.b $2$ $3.793$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$0$$ $$8$$ $$q+(-2+2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+4q^{7}+\cdots$$
475.2.e.c $2$ $3.793$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$0$$ $$8$$ $$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+4q^{7}+3\zeta_{6}q^{9}+\cdots$$
475.2.e.d $6$ $3.793$ 6.0.3518667.1 None $$1$$ $$1$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(-3+\cdots)q^{4}+\cdots$$
475.2.e.e $8$ $3.793$ 8.0.4601315889.1 None $$1$$ $$3$$ $$0$$ $$8$$ $$q-\beta _{7}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$$
475.2.e.f $12$ $3.793$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-2$$ $$-3$$ $$0$$ $$4$$ $$q+(\beta _{7}+\beta _{8})q^{2}+(1-\beta _{1}+\beta _{2}+\beta _{9}+\cdots)q^{3}+\cdots$$
475.2.e.g $12$ $3.793$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+(\beta _{4}-\beta _{5})q^{3}+(\beta _{2}-\beta _{3}+\beta _{8}+\cdots)q^{4}+\cdots$$
475.2.e.h $12$ $3.793$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$2$$ $$3$$ $$0$$ $$-4$$ $$q+(-\beta _{7}-\beta _{8})q^{2}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$$

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

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