# Properties

 Label 275.2.b Level $275$ Weight $2$ Character orbit 275.b Rep. character $\chi_{275}(199,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $5$ Sturm bound $60$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$275 = 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 275.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$60$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(275, [\chi])$$.

Total New Old
Modular forms 36 16 20
Cusp forms 24 16 8
Eisenstein series 12 0 12

## Trace form

 $$16 q - 10 q^{4} - 16 q^{6} - 14 q^{9} + O(q^{10})$$ $$16 q - 10 q^{4} - 16 q^{6} - 14 q^{9} + 4 q^{11} - 4 q^{14} - 10 q^{16} + 12 q^{19} - 16 q^{21} + 20 q^{24} + 16 q^{26} + 8 q^{29} - 2 q^{31} - 12 q^{34} + 22 q^{36} - 4 q^{39} - 8 q^{41} - 2 q^{44} - 24 q^{46} + 4 q^{49} + 12 q^{51} + 12 q^{54} + 36 q^{56} + 6 q^{59} - 20 q^{61} + 30 q^{64} + 8 q^{66} + 6 q^{69} + 2 q^{71} - 8 q^{74} - 28 q^{76} - 20 q^{84} - 56 q^{86} - 6 q^{89} + 44 q^{91} - 48 q^{96} - 22 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(275, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
275.2.b.a $2$ $2.196$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}+2iq^{7}+\cdots$$
275.2.b.b $2$ $2.196$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}+3iq^{8}+3q^{9}-q^{11}+\cdots$$
275.2.b.c $4$ $2.196$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-2+\beta _{3})q^{4}+\cdots$$
275.2.b.d $4$ $2.196$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{2}+(\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots$$
275.2.b.e $4$ $2.196$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(275, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(275, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 2}$$