# Properties

 Label 108.4.b Level $108$ Weight $4$ Character orbit 108.b Rep. character $\chi_{108}(107,\cdot)$ Character field $\Q$ Dimension $24$ Newform subspaces $2$ Sturm bound $72$ Trace bound $4$

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## Defining parameters

 Level: $$N$$ $$=$$ $$108 = 2^{2} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 108.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$12$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$72$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(108, [\chi])$$.

Total New Old
Modular forms 60 24 36
Cusp forms 48 24 24
Eisenstein series 12 0 12

## Trace form

 $$24 q - 6 q^{4} + O(q^{10})$$ $$24 q - 6 q^{4} + 66 q^{10} - 36 q^{13} + 138 q^{16} + 186 q^{22} - 516 q^{25} + 138 q^{28} - 684 q^{34} + 276 q^{37} - 378 q^{40} + 1056 q^{46} - 432 q^{49} + 1128 q^{52} + 1884 q^{58} - 828 q^{61} - 570 q^{64} - 5406 q^{70} + 816 q^{73} - 4428 q^{76} + 1944 q^{82} + 888 q^{85} + 8190 q^{88} + 4164 q^{94} + 3048 q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(108, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
108.4.b.a $12$ $6.372$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}+(-1-\beta _{4})q^{4}-\beta _{9}q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$$
108.4.b.b $12$ $6.372$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}-\beta _{6}q^{4}+\beta _{5}q^{5}-\beta _{4}q^{7}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(108, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(108, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 2}$$