# Properties

 Label 132.2.h Level $132$ Weight $2$ Character orbit 132.h Rep. character $\chi_{132}(43,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $1$ Sturm bound $48$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$132 = 2^{2} \cdot 3 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 132.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$44$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$48$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(132, [\chi])$$.

Total New Old
Modular forms 28 12 16
Cusp forms 20 12 8
Eisenstein series 8 0 8

## Trace form

 $$12 q + 4 q^{4} - 12 q^{9} + O(q^{10})$$ $$12 q + 4 q^{4} - 12 q^{9} - 8 q^{12} + 4 q^{14} + 4 q^{16} - 28 q^{20} - 4 q^{22} + 20 q^{25} - 12 q^{26} + 4 q^{33} + 40 q^{34} - 4 q^{36} - 32 q^{37} - 8 q^{38} - 12 q^{42} + 36 q^{44} + 16 q^{48} - 12 q^{49} - 16 q^{53} - 20 q^{56} + 24 q^{58} + 12 q^{60} - 20 q^{64} + 8 q^{66} - 64 q^{70} + 48 q^{77} + 20 q^{78} + 52 q^{80} + 12 q^{81} - 32 q^{82} + 72 q^{86} + 12 q^{88} - 8 q^{89} - 12 q^{92} + 16 q^{93} - 48 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(132, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
132.2.h.a $12$ $1.054$ 12.0.$$\cdots$$.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{2}+\beta _{3})q^{4}+(\beta _{6}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(132, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(132, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(44, [\chi])$$$$^{\oplus 2}$$