# Properties

 Label 2151.1.d Level $2151$ Weight $1$ Character orbit 2151.d Rep. character $\chi_{2151}(955,\cdot)$ Character field $\Q$ Dimension $11$ Newform subspaces $5$ Sturm bound $240$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2151 = 3^{2} \cdot 239$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2151.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$239$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$240$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2151, [\chi])$$.

Total New Old
Modular forms 36 12 24
Cusp forms 32 11 21
Eisenstein series 4 1 3

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 7 0 4 0

## Trace form

 $$11q + q^{2} + 6q^{4} + q^{5} + 2q^{8} + O(q^{10})$$ $$11q + q^{2} + 6q^{4} + q^{5} + 2q^{8} - 6q^{10} + q^{11} + q^{16} + q^{17} + 3q^{20} - 6q^{22} + 6q^{25} + q^{29} - 5q^{31} + 3q^{32} - 6q^{34} + 3q^{44} + 3q^{49} + 3q^{50} + 2q^{55} - 6q^{58} + 3q^{61} - 13q^{62} + 8q^{64} - 5q^{67} + 3q^{68} + q^{71} - 10q^{80} + q^{83} + 2q^{85} + 8q^{91} + q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2151, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2151.1.d.a $$1$$ $$1.073$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-239})$$ None $$1$$ $$0$$ $$1$$ $$0$$ $$q+q^{2}+q^{5}-q^{8}+q^{10}+q^{11}-q^{16}+\cdots$$
2151.1.d.b $$2$$ $$1.073$$ $$\Q(\sqrt{-2})$$ $$S_{4}$$ None None $$-2$$ $$0$$ $$2$$ $$0$$ $$q-q^{2}+q^{5}-\beta q^{7}+q^{8}-q^{10}+q^{11}+\cdots$$
2151.1.d.c $$2$$ $$1.073$$ $$\Q(\sqrt{5})$$ $$D_{5}$$ $$\Q(\sqrt{-239})$$ None $$1$$ $$0$$ $$1$$ $$0$$ $$q+(1-\beta )q^{2}+(1-\beta )q^{4}+(1-\beta )q^{5}+\cdots$$
2151.1.d.d $$2$$ $$1.073$$ $$\Q(\sqrt{-2})$$ $$S_{4}$$ None None $$2$$ $$0$$ $$-2$$ $$0$$ $$q+q^{2}-q^{5}-\beta q^{7}-q^{8}-q^{10}-q^{11}+\cdots$$
2151.1.d.e $$4$$ $$1.073$$ $$\Q(\zeta_{15})^+$$ $$D_{15}$$ $$\Q(\sqrt{-239})$$ None $$-1$$ $$0$$ $$-1$$ $$0$$ $$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(2151, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(2151, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(239, [\chi])$$$$^{\oplus 3}$$