# Properties

 Label 1476.1.h Level $1476$ Weight $1$ Character orbit 1476.h Rep. character $\chi_{1476}(163,\cdot)$ Character field $\Q$ Dimension $3$ Newform subspaces $2$ Sturm bound $252$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1476 = 2^{2} \cdot 3^{2} \cdot 41$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1476.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$164$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$252$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1476, [\chi])$$.

Total New Old
Modular forms 20 5 15
Cusp forms 12 3 9
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 3 0 0 0

## Trace form

 $$3 q + q^{2} + 3 q^{4} + 2 q^{5} + q^{8} + O(q^{10})$$ $$3 q + q^{2} + 3 q^{4} + 2 q^{5} + q^{8} - 2 q^{10} + 3 q^{16} + 2 q^{20} + q^{25} + q^{32} - 2 q^{37} - 2 q^{40} - 3 q^{41} + q^{49} - 5 q^{50} - 2 q^{61} + 3 q^{64} - 2 q^{73} + 2 q^{74} - 4 q^{77} + 2 q^{80} - q^{82} + 3 q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1476, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1476.1.h.a $$1$$ $$0.737$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-41})$$ $$\Q(\sqrt{41})$$ $$-1$$ $$0$$ $$2$$ $$0$$ $$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{16}+\cdots$$
1476.1.h.b $$2$$ $$0.737$$ $$\Q(\sqrt{2})$$ $$D_{4}$$ $$\Q(\sqrt{-41})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}-\beta q^{7}+q^{8}+\beta q^{11}-\beta q^{14}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(1476, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(1476, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(164, [\chi])$$$$^{\oplus 3}$$