# Properties

 Label 495.2.c Level $495$ Weight $2$ Character orbit 495.c Rep. character $\chi_{495}(199,\cdot)$ Character field $\Q$ Dimension $24$ Newform subspaces $5$ Sturm bound $144$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$495 = 3^{2} \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 495.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$144$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$2$$, $$29$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(495, [\chi])$$.

Total New Old
Modular forms 80 24 56
Cusp forms 64 24 40
Eisenstein series 16 0 16

## Trace form

 $$24 q - 18 q^{4} - q^{5} + O(q^{10})$$ $$24 q - 18 q^{4} - q^{5} - 6 q^{10} + 4 q^{11} + 4 q^{14} + 10 q^{16} + 16 q^{19} + 8 q^{20} + 5 q^{25} + 24 q^{26} + 12 q^{29} - 30 q^{31} - 40 q^{34} - 18 q^{35} + 8 q^{40} - 12 q^{41} - 14 q^{44} + 56 q^{46} - 24 q^{49} + 10 q^{50} + 3 q^{55} - 36 q^{56} - 18 q^{59} - 4 q^{61} - 14 q^{64} - 40 q^{65} + 32 q^{70} + 54 q^{71} - 44 q^{74} - 40 q^{76} + 20 q^{79} + 46 q^{80} + 10 q^{85} + 28 q^{86} + 34 q^{89} - 12 q^{94} + 36 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(495, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
495.2.c.a $4$ $3.953$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$0$$ $$3$$ $$0$$ $$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$$
495.2.c.b $4$ $3.953$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots$$
495.2.c.c $4$ $3.953$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots$$
495.2.c.d $6$ $3.953$ 6.0.350464.1 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-\beta _{1}-\beta _{3}-\beta _{5})q^{2}+(-2+\beta _{1}+\cdots)q^{4}+\cdots$$
495.2.c.e $6$ $3.953$ 6.0.350464.1 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta _{4}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(495, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(495, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(165, [\chi])$$$$^{\oplus 2}$$