# Properties

 Label 108.3.d Level $108$ Weight $3$ Character orbit 108.d Rep. character $\chi_{108}(55,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $4$ Sturm bound $54$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$108 = 2^{2} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 108.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$54$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(108, [\chi])$$.

Total New Old
Modular forms 42 16 26
Cusp forms 30 16 14
Eisenstein series 12 0 12

## Trace form

 $$16 q - 2 q^{4} + O(q^{10})$$ $$16 q - 2 q^{4} + 14 q^{10} + 8 q^{13} + 10 q^{16} - 102 q^{22} + 72 q^{25} - 150 q^{28} - 40 q^{34} + 8 q^{37} + 170 q^{40} + 372 q^{46} - 176 q^{49} + 44 q^{52} - 340 q^{58} - 184 q^{61} - 326 q^{64} - 78 q^{70} - 64 q^{73} + 576 q^{76} + 596 q^{82} + 400 q^{85} + 342 q^{88} - 300 q^{94} + 128 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(108, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
108.3.d.a $2$ $2.943$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$14$$ $$0$$ $$q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{4}+7q^{5}+\cdots$$
108.3.d.b $2$ $2.943$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-14$$ $$0$$ $$q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{4}-7q^{5}+\cdots$$
108.3.d.c $4$ $2.943$ $$\Q(\sqrt{-3}, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}-\beta _{2})q^{2}+(3+\beta _{3})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$$
108.3.d.d $8$ $2.943$ 8.0.207360000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(-1+\beta _{5})q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(108, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(108, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 2}$$