# Properties

 Label 840.2.t Level $840$ Weight $2$ Character orbit 840.t Rep. character $\chi_{840}(169,\cdot)$ Character field $\Q$ Dimension $20$ Newform subspaces $5$ Sturm bound $384$ Trace bound $15$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$840 = 2^{3} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 840.t (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$384$$ Trace bound: $$15$$ Distinguishing $$T_p$$: $$11$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(840, [\chi])$$.

Total New Old
Modular forms 208 20 188
Cusp forms 176 20 156
Eisenstein series 32 0 32

## Trace form

 $$20 q - 8 q^{5} - 20 q^{9} + O(q^{10})$$ $$20 q - 8 q^{5} - 20 q^{9} + 4 q^{21} + 4 q^{25} + 32 q^{29} - 8 q^{31} + 8 q^{39} - 32 q^{41} + 8 q^{45} - 20 q^{49} - 24 q^{51} + 8 q^{55} - 32 q^{61} + 24 q^{71} + 16 q^{79} + 20 q^{81} - 16 q^{85} + 48 q^{89} - 24 q^{91} + 8 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(840, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
840.2.t.a $2$ $6.707$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-iq^{3}+(-1-2i)q^{5}-iq^{7}-q^{9}+\cdots$$
840.2.t.b $2$ $6.707$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-iq^{3}+(-1+2i)q^{5}-iq^{7}-q^{9}+\cdots$$
840.2.t.c $4$ $6.707$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{1}q^{7}-q^{9}-2q^{11}+\cdots$$
840.2.t.d $6$ $6.707$ 6.0.350464.1 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{1}q^{7}-q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$$
840.2.t.e $6$ $6.707$ 6.0.350464.1 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}-q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(840, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(840, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(420, [\chi])$$$$^{\oplus 2}$$