# Properties

 Label 4140.2.i Level $4140$ Weight $2$ Character orbit 4140.i Rep. character $\chi_{4140}(1241,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $2$ Sturm bound $1728$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4140.i (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$69$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$1728$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(4140, [\chi])$$.

Total New Old
Modular forms 888 32 856
Cusp forms 840 32 808
Eisenstein series 48 0 48

## Trace form

 $$32 q + O(q^{10})$$ $$32 q + 32 q^{25} - 16 q^{31} - 80 q^{49} + 16 q^{73} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(4140, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4140.2.i.a $16$ $33.058$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$-16$$ $$0$$ $$q-q^{5}-\beta _{9}q^{7}+\beta _{1}q^{11}-\beta _{5}q^{13}+\cdots$$
4140.2.i.b $16$ $33.058$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$16$$ $$0$$ $$q+q^{5}-\beta _{9}q^{7}-\beta _{1}q^{11}-\beta _{5}q^{13}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(4140, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(4140, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(69, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(138, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(207, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(276, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(345, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(414, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(690, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(828, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1035, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1380, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2070, [\chi])$$$$^{\oplus 2}$$