# Properties

 Label 36.6.h Level 36 Weight 6 Character orbit h Rep. character $$\chi_{36}(11,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 56 Newform subspaces 1 Sturm bound 36 Trace bound 0

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## Defining parameters

 Level: $$N$$ $$=$$ $$36 = 2^{2} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 36.h (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$36$$ Character field: $$\Q(\zeta_{6})$$ 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 64 64 0
Cusp forms 56 56 0
Eisenstein series 8 8 0

## Trace form

 $$56q - 3q^{2} - q^{4} - 6q^{5} - 27q^{6} + 18q^{9} + O(q^{10})$$ $$56q - 3q^{2} - q^{4} - 6q^{5} - 27q^{6} + 18q^{9} - 68q^{10} - 486q^{12} - 2q^{13} - 1518q^{14} - q^{16} + 1992q^{18} - 1242q^{20} + 330q^{21} + 63q^{22} + 2235q^{24} + 12498q^{25} - 2052q^{28} - 11946q^{29} - 6882q^{30} - 7233q^{32} + 17040q^{33} + 6361q^{34} + 6399q^{36} - 8q^{37} - 14877q^{38} - 1526q^{40} - 43536q^{41} + 18564q^{42} - 42q^{45} - 26880q^{46} - 5931q^{48} + 38414q^{49} + 38631q^{50} + 24988q^{52} + 37587q^{54} + 21186q^{56} - 90786q^{57} - 3314q^{58} + 60930q^{60} - 2q^{61} - 106342q^{64} + 35970q^{65} - 47838q^{66} + 31413q^{68} - 1854q^{69} + 10524q^{70} - 130941q^{72} + 53620q^{73} - 20406q^{74} + 26193q^{76} + 26178q^{77} - 96684q^{78} - 14790q^{81} - 151286q^{82} + 141630q^{84} + 6248q^{85} + 279237q^{86} - 122541q^{88} + 235278q^{90} + 435804q^{92} + 71838q^{93} + 63480q^{94} - 37476q^{96} - 58148q^{97} + O(q^{100})$$

## 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.h.a $$56$$ $$5.774$$ None $$-3$$ $$0$$ $$-6$$ $$0$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database