# Properties

 Label 36.6.e Level $36$ Weight $6$ Character orbit 36.e Rep. character $\chi_{36}(13,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $10$ Newform subspaces $1$ Sturm bound $36$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$36 = 2^{2} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$6$$ 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: $$36$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(36, [\chi])$$.

Total New Old
Modular forms 66 10 56
Cusp forms 54 10 44
Eisenstein series 12 0 12

## Trace form

 $$10q + 12q^{3} - 21q^{5} + 29q^{7} + 12q^{9} + O(q^{10})$$ $$10q + 12q^{3} - 21q^{5} + 29q^{7} + 12q^{9} + 177q^{11} - 181q^{13} + 117q^{15} + 2280q^{17} - 832q^{19} - 207q^{21} + 399q^{23} - 4778q^{25} - 7128q^{27} - 6033q^{29} + 2759q^{31} + 9603q^{33} + 37146q^{35} - 15172q^{37} + 5529q^{39} - 18435q^{41} + 1469q^{43} - 64089q^{45} - 25155q^{47} - 4056q^{49} + 90612q^{51} + 116844q^{53} + 14778q^{55} + 26934q^{57} - 90537q^{59} + 1403q^{61} - 198255q^{63} - 148407q^{65} + 13907q^{67} + 214425q^{69} + 229368q^{71} + 15200q^{73} + 44640q^{75} - 211983q^{77} + 29993q^{79} - 404172q^{81} - 228951q^{83} - 49662q^{85} + 397323q^{87} + 598332q^{89} + 124930q^{91} + 250041q^{93} - 394764q^{95} + 40541q^{97} - 697239q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(36, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
36.6.e.a $$10$$ $$5.774$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$12$$ $$-21$$ $$29$$ $$q+(2+2\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(4\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(36, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(36, [\chi]) \cong$$ $$S_{6}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 2}$$