# Properties

 Label 1840.2.i Level $1840$ Weight $2$ Character orbit 1840.i Rep. character $\chi_{1840}(1471,\cdot)$ Character field $\Q$ Dimension $48$ Newform subspaces $3$ Sturm bound $576$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1840 = 2^{4} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1840.i (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$92$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$576$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1840, [\chi])$$.

Total New Old
Modular forms 300 48 252
Cusp forms 276 48 228
Eisenstein series 24 0 24

## Trace form

 $$48 q - 48 q^{9} + O(q^{10})$$ $$48 q - 48 q^{9} - 48 q^{25} + 24 q^{29} - 24 q^{41} + 24 q^{49} + 60 q^{69} - 96 q^{77} + 72 q^{81} + 96 q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1840, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1840.2.i.a $16$ $14.692$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{8}q^{5}+(\beta _{3}-\beta _{10})q^{7}+(-2+\cdots)q^{9}+\cdots$$
1840.2.i.b $16$ $14.692$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{7}q^{3}+\beta _{2}q^{5}+\beta _{13}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots$$
1840.2.i.c $16$ $14.692$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}+\beta _{5}q^{5}+(-\beta _{10}+\beta _{14})q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1840, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1840, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(92, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(184, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(368, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(460, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(920, [\chi])$$$$^{\oplus 2}$$