# Properties

 Label 36.4.e Level $36$ Weight $4$ Character orbit 36.e Rep. character $\chi_{36}(13,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $6$ Newform subspaces $1$ Sturm bound $24$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$36 = 2^{2} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 36.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$1$$ Sturm bound: $$24$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(36, [\chi])$$.

Total New Old
Modular forms 42 6 36
Cusp forms 30 6 24
Eisenstein series 12 0 12

## Trace form

 $$6 q - 3 q^{3} + 6 q^{5} - 6 q^{7} + 39 q^{9} + O(q^{10})$$ $$6 q - 3 q^{3} + 6 q^{5} - 6 q^{7} + 39 q^{9} + 51 q^{11} + 12 q^{13} - 180 q^{15} - 222 q^{17} + 30 q^{19} - 120 q^{21} + 210 q^{23} - 3 q^{25} + 648 q^{27} + 456 q^{29} + 48 q^{31} - 603 q^{33} - 1104 q^{35} - 96 q^{37} - 36 q^{39} + 897 q^{41} + 129 q^{43} + 1494 q^{45} + 522 q^{47} - 225 q^{49} - 1647 q^{51} - 2208 q^{53} - 216 q^{55} - 645 q^{57} + 453 q^{59} - 402 q^{61} + 1896 q^{63} + 1110 q^{65} - 213 q^{67} - 198 q^{69} + 120 q^{71} + 750 q^{73} + 921 q^{75} + 1128 q^{77} + 552 q^{79} - 549 q^{81} - 612 q^{83} + 1188 q^{85} - 1386 q^{87} - 924 q^{89} - 264 q^{91} - 1998 q^{93} - 2184 q^{95} + 93 q^{97} - 1854 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(36, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
36.4.e.a $6$ $2.124$ 6.0.6831243.2 None $$0$$ $$-3$$ $$6$$ $$-6$$ $$q+(-1-\beta _{2})q^{3}+(1-3\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(36, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(36, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 2}$$