# Properties

 Label 495.2.n Level $495$ Weight $2$ Character orbit 495.n Rep. character $\chi_{495}(91,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $80$ Newform subspaces $8$ Sturm bound $144$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$495 = 3^{2} \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 495.n (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$8$$ Sturm bound: $$144$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 320 80 240
Cusp forms 256 80 176
Eisenstein series 64 0 64

## Trace form

 $$80 q - 2 q^{2} - 24 q^{4} - 4 q^{7} + 14 q^{8} + O(q^{10})$$ $$80 q - 2 q^{2} - 24 q^{4} - 4 q^{7} + 14 q^{8} + 8 q^{10} + 6 q^{11} + 2 q^{13} - 16 q^{16} + 28 q^{17} + 14 q^{19} - 4 q^{20} - 62 q^{22} + 16 q^{23} - 20 q^{25} - 20 q^{26} + 22 q^{28} - 18 q^{29} - 12 q^{31} - 84 q^{32} - 16 q^{34} + 4 q^{35} + 20 q^{37} + 42 q^{38} - 6 q^{40} + 24 q^{41} + 20 q^{43} - 12 q^{44} + 18 q^{46} + 28 q^{47} + 2 q^{49} - 2 q^{50} + 58 q^{52} - 32 q^{53} - 12 q^{55} - 52 q^{56} - 26 q^{58} - 18 q^{59} - 52 q^{61} + 52 q^{62} - 28 q^{64} - 40 q^{65} - 8 q^{67} - 6 q^{68} - 40 q^{70} - 44 q^{71} - 42 q^{73} + 16 q^{74} - 112 q^{76} + 86 q^{77} - 2 q^{79} - 32 q^{80} + 54 q^{82} + 2 q^{83} - 16 q^{85} + 90 q^{86} + 98 q^{88} + 48 q^{89} - 48 q^{91} - 12 q^{92} - 6 q^{94} + 16 q^{95} + 60 q^{97} - 28 q^{98} + O(q^{100})$$

## 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.n.a $8$ $3.953$ 8.0.13140625.1 None $$-4$$ $$0$$ $$2$$ $$3$$ $$q+(-1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$$
495.2.n.b $8$ $3.953$ 8.0.819390625.1 None $$-2$$ $$0$$ $$-2$$ $$9$$ $$q-\beta _{4}q^{2}+(1-\beta _{1}+2\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$$
495.2.n.c $8$ $3.953$ $$\Q(\zeta_{15})$$ None $$-2$$ $$0$$ $$2$$ $$-5$$ $$q+(1-2\zeta_{15}+\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots$$
495.2.n.d $8$ $3.953$ 8.0.13140625.1 None $$0$$ $$0$$ $$-2$$ $$1$$ $$q+(-1+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6})q^{2}+(-2\beta _{2}+\cdots)q^{4}+\cdots$$
495.2.n.e $8$ $3.953$ 8.0.13140625.1 None $$2$$ $$0$$ $$-2$$ $$-1$$ $$q+\beta _{6}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{6}-\beta _{7})q^{4}+\cdots$$
495.2.n.f $8$ $3.953$ 8.0.159390625.1 None $$4$$ $$0$$ $$2$$ $$-3$$ $$q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$$
495.2.n.g $16$ $3.953$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-2$$ $$0$$ $$-4$$ $$-4$$ $$q+(1-\beta _{1}+\beta _{3}+\beta _{5}-\beta _{10}-\beta _{14}+\cdots)q^{2}+\cdots$$
495.2.n.h $16$ $3.953$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$2$$ $$0$$ $$4$$ $$-4$$ $$q+(-1+\beta _{1}-\beta _{3}-\beta _{5}+\beta _{10}+\beta _{14}+\cdots)q^{2}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(495, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(99, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(165, [\chi])$$$$^{\oplus 2}$$