Properties

 Label 2888.1.u Level $2888$ Weight $1$ Character orbit 2888.u Rep. character $\chi_{2888}(99,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $42$ Newform subspaces $7$ Sturm bound $380$ Trace bound $22$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$2888 = 2^{3} \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2888.u (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$152$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$7$$ Sturm bound: $$380$$ Trace bound: $$22$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2888, [\chi])$$.

Total New Old
Modular forms 174 138 36
Cusp forms 54 42 12
Eisenstein series 120 96 24

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 42 0 0 0

Trace form

 $$42 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9} + O(q^{10})$$ $$42 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9} + 6 q^{11} - 6 q^{18} - 6 q^{22} + 3 q^{24} - 3 q^{27} + 3 q^{33} + 3 q^{36} + 3 q^{41} - 6 q^{44} - 6 q^{48} - 21 q^{49} + 3 q^{50} - 3 q^{51} + 3 q^{54} + 3 q^{59} - 21 q^{64} + 3 q^{66} + 3 q^{67} + 3 q^{68} - 6 q^{72} - 6 q^{73} - 3 q^{81} + 3 q^{82} + 6 q^{83} - 12 q^{96} + 3 q^{97} - 3 q^{99} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(2888, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2888.1.u.a $6$ $1.441$ $$\Q(\zeta_{18})$$ $D_{9}$ $$\Q(\sqrt{-2})$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+\zeta_{18}^{5}q^{2}+(-1-\zeta_{18}^{4})q^{3}-\zeta_{18}q^{4}+\cdots$$
2888.1.u.b $6$ $1.441$ $$\Q(\zeta_{18})$$ $D_{9}$ $$\Q(\sqrt{-2})$$ None $$0$$ $$-3$$ $$0$$ $$0$$ $$q-\zeta_{18}^{5}q^{2}+(-\zeta_{18}-\zeta_{18}^{3})q^{3}-\zeta_{18}q^{4}+\cdots$$
2888.1.u.c $6$ $1.441$ $$\Q(\zeta_{18})$$ $D_{3}$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{6}+\cdots$$
2888.1.u.d $6$ $1.441$ $$\Q(\zeta_{18})$$ $D_{3}$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{18}^{5}q^{2}+\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{6}+\cdots$$
2888.1.u.e $6$ $1.441$ $$\Q(\zeta_{18})$$ $D_{9}$ $$\Q(\sqrt{-2})$$ None $$0$$ $$3$$ $$0$$ $$0$$ $$q+\zeta_{18}^{5}q^{2}+(-\zeta_{18}^{6}+\zeta_{18}^{7})q^{3}+\cdots$$
2888.1.u.f $6$ $1.441$ $$\Q(\zeta_{18})$$ $D_{9}$ $$\Q(\sqrt{-2})$$ None $$0$$ $$3$$ $$0$$ $$0$$ $$q+\zeta_{18}^{5}q^{2}+(\zeta_{18}+\zeta_{18}^{3})q^{3}-\zeta_{18}q^{4}+\cdots$$
2888.1.u.g $6$ $1.441$ $$\Q(\zeta_{18})$$ $D_{9}$ $$\Q(\sqrt{-2})$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q-\zeta_{18}^{5}q^{2}+(1+\zeta_{18}^{4})q^{3}-\zeta_{18}q^{4}+\cdots$$

Decomposition of $$S_{1}^{\mathrm{old}}(2888, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(2888, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(152, [\chi])$$$$^{\oplus 2}$$