# Properties

 Label 1665.2.c Level $1665$ Weight $2$ Character orbit 1665.c Rep. character $\chi_{1665}(334,\cdot)$ Character field $\Q$ Dimension $90$ Newform subspaces $7$ Sturm bound $456$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1665 = 3^{2} \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1665.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$456$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1665, [\chi])$$.

Total New Old
Modular forms 236 90 146
Cusp forms 220 90 130
Eisenstein series 16 0 16

## Trace form

 $$90 q - 86 q^{4} + 2 q^{5} + O(q^{10})$$ $$90 q - 86 q^{4} + 2 q^{5} - 18 q^{10} - 8 q^{11} + 102 q^{16} + 8 q^{19} - 4 q^{20} + 14 q^{25} - 12 q^{26} + 12 q^{29} - 12 q^{31} - 28 q^{34} + 6 q^{35} + 50 q^{40} - 4 q^{41} + 24 q^{44} + 16 q^{46} - 122 q^{49} + 36 q^{50} - 18 q^{55} - 24 q^{56} - 20 q^{59} - 16 q^{61} - 110 q^{64} + 4 q^{65} + 32 q^{70} + 8 q^{71} - 10 q^{74} - 32 q^{76} + 20 q^{79} + 52 q^{80} + 32 q^{85} - 80 q^{86} - 16 q^{89} + 76 q^{91} + 52 q^{94} + 20 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1665, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1665.2.c.a $2$ $13.295$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+2iq^{2}-2q^{4}+(1+2i)q^{5}+(-4+\cdots)q^{10}+\cdots$$
1665.2.c.b $2$ $13.295$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+2q^{4}+(-1+2i)q^{5}+2iq^{7}-6q^{11}+\cdots$$
1665.2.c.c $2$ $13.295$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+2q^{4}+(1+2i)q^{5}-2iq^{7}+6q^{11}+\cdots$$
1665.2.c.d $8$ $13.295$ 8.0.309760000.3 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{4}+\beta _{5})q^{2}+(1-\beta _{1})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$$
1665.2.c.e $18$ $13.295$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(\beta _{1}+\beta _{13})q^{2}+(-2+\beta _{3}+\beta _{4})q^{4}+\cdots$$
1665.2.c.f $26$ $13.295$ None $$0$$ $$0$$ $$2$$ $$0$$
1665.2.c.g $32$ $13.295$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1665, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1665, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(185, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(555, [\chi])$$$$^{\oplus 2}$$