# Properties

 Label 612.1.e Level $612$ Weight $1$ Character orbit 612.e Rep. character $\chi_{612}(271,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $108$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$612 = 2^{2} \cdot 3^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 612.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$68$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$108$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(612, [\chi])$$.

Total New Old
Modular forms 12 3 9
Cusp forms 4 1 3
Eisenstein series 8 2 6

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 1 0 0 0

## Trace form

 $$q + q^{2} + q^{4} + q^{8} + O(q^{10})$$ $$q + q^{2} + q^{4} + q^{8} - 2 q^{13} + q^{16} - q^{17} + q^{25} - 2 q^{26} + q^{32} - q^{34} - q^{49} + q^{50} - 2 q^{52} - 2 q^{53} + q^{64} - q^{68} + 2 q^{89} - q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(612, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
612.1.e.a $1$ $0.305$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-17})$$ $$\Q(\sqrt{17})$$ $$1$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}+q^{8}-2q^{13}+q^{16}-q^{17}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(612, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(612, [\chi]) \simeq$$ $$S_{1}^{\mathrm{new}}(68, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(204, [\chi])$$$$^{\oplus 2}$$