Properties

 Label 18.4.c Level 18 Weight 4 Character orbit c Rep. character $$\chi_{18}(7,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 6 Newforms 2 Sturm bound 12 Trace bound 1

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Defining parameters

 Level: $$N$$ = $$18 = 2 \cdot 3^{2}$$ Weight: $$k$$ = $$4$$ Character orbit: $$[\chi]$$ = 18.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$9$$ Character field: $$\Q(\zeta_{3})$$ Newforms: $$2$$ Sturm bound: $$12$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(18, [\chi])$$.

Total New Old
Modular forms 22 6 16
Cusp forms 14 6 8
Eisenstein series 8 0 8

Trace form

 $$6q$$ $$\mathstrut +\mathstrut 2q^{2}$$ $$\mathstrut +\mathstrut 3q^{3}$$ $$\mathstrut -\mathstrut 12q^{4}$$ $$\mathstrut +\mathstrut 18q^{5}$$ $$\mathstrut -\mathstrut 18q^{6}$$ $$\mathstrut +\mathstrut 12q^{7}$$ $$\mathstrut -\mathstrut 16q^{8}$$ $$\mathstrut -\mathstrut 105q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$6q$$ $$\mathstrut +\mathstrut 2q^{2}$$ $$\mathstrut +\mathstrut 3q^{3}$$ $$\mathstrut -\mathstrut 12q^{4}$$ $$\mathstrut +\mathstrut 18q^{5}$$ $$\mathstrut -\mathstrut 18q^{6}$$ $$\mathstrut +\mathstrut 12q^{7}$$ $$\mathstrut -\mathstrut 16q^{8}$$ $$\mathstrut -\mathstrut 105q^{9}$$ $$\mathstrut +\mathstrut 39q^{11}$$ $$\mathstrut +\mathstrut 24q^{12}$$ $$\mathstrut -\mathstrut 24q^{13}$$ $$\mathstrut +\mathstrut 100q^{14}$$ $$\mathstrut +\mathstrut 90q^{15}$$ $$\mathstrut -\mathstrut 48q^{16}$$ $$\mathstrut -\mathstrut 78q^{17}$$ $$\mathstrut +\mathstrut 156q^{18}$$ $$\mathstrut +\mathstrut 210q^{19}$$ $$\mathstrut +\mathstrut 72q^{20}$$ $$\mathstrut -\mathstrut 36q^{21}$$ $$\mathstrut -\mathstrut 18q^{22}$$ $$\mathstrut -\mathstrut 264q^{23}$$ $$\mathstrut -\mathstrut 24q^{24}$$ $$\mathstrut -\mathstrut 219q^{25}$$ $$\mathstrut -\mathstrut 392q^{26}$$ $$\mathstrut -\mathstrut 96q^{28}$$ $$\mathstrut -\mathstrut 348q^{29}$$ $$\mathstrut -\mathstrut 288q^{30}$$ $$\mathstrut -\mathstrut 6q^{31}$$ $$\mathstrut +\mathstrut 32q^{32}$$ $$\mathstrut +\mathstrut 765q^{33}$$ $$\mathstrut +\mathstrut 90q^{34}$$ $$\mathstrut +\mathstrut 1332q^{35}$$ $$\mathstrut +\mathstrut 516q^{36}$$ $$\mathstrut +\mathstrut 192q^{37}$$ $$\mathstrut +\mathstrut 322q^{38}$$ $$\mathstrut -\mathstrut 582q^{39}$$ $$\mathstrut -\mathstrut 207q^{41}$$ $$\mathstrut -\mathstrut 816q^{42}$$ $$\mathstrut +\mathstrut 129q^{43}$$ $$\mathstrut -\mathstrut 312q^{44}$$ $$\mathstrut -\mathstrut 702q^{45}$$ $$\mathstrut +\mathstrut 504q^{46}$$ $$\mathstrut -\mathstrut 660q^{47}$$ $$\mathstrut -\mathstrut 144q^{48}$$ $$\mathstrut -\mathstrut 585q^{49}$$ $$\mathstrut +\mathstrut 614q^{50}$$ $$\mathstrut -\mathstrut 153q^{51}$$ $$\mathstrut -\mathstrut 96q^{52}$$ $$\mathstrut +\mathstrut 528q^{53}$$ $$\mathstrut +\mathstrut 954q^{54}$$ $$\mathstrut -\mathstrut 1404q^{55}$$ $$\mathstrut +\mathstrut 400q^{56}$$ $$\mathstrut +\mathstrut 987q^{57}$$ $$\mathstrut +\mathstrut 252q^{58}$$ $$\mathstrut -\mathstrut 327q^{59}$$ $$\mathstrut -\mathstrut 936q^{60}$$ $$\mathstrut +\mathstrut 858q^{61}$$ $$\mathstrut -\mathstrut 1664q^{62}$$ $$\mathstrut -\mathstrut 1794q^{63}$$ $$\mathstrut +\mathstrut 384q^{64}$$ $$\mathstrut +\mathstrut 414q^{65}$$ $$\mathstrut +\mathstrut 288q^{66}$$ $$\mathstrut +\mathstrut 1587q^{67}$$ $$\mathstrut +\mathstrut 156q^{68}$$ $$\mathstrut +\mathstrut 1494q^{69}$$ $$\mathstrut +\mathstrut 216q^{70}$$ $$\mathstrut -\mathstrut 312q^{71}$$ $$\mathstrut -\mathstrut 24q^{72}$$ $$\mathstrut -\mathstrut 258q^{73}$$ $$\mathstrut +\mathstrut 856q^{74}$$ $$\mathstrut +\mathstrut 3231q^{75}$$ $$\mathstrut -\mathstrut 420q^{76}$$ $$\mathstrut +\mathstrut 708q^{77}$$ $$\mathstrut +\mathstrut 132q^{78}$$ $$\mathstrut -\mathstrut 1482q^{79}$$ $$\mathstrut -\mathstrut 576q^{80}$$ $$\mathstrut +\mathstrut 315q^{81}$$ $$\mathstrut -\mathstrut 2916q^{82}$$ $$\mathstrut -\mathstrut 138q^{83}$$ $$\mathstrut +\mathstrut 744q^{84}$$ $$\mathstrut +\mathstrut 108q^{85}$$ $$\mathstrut -\mathstrut 86q^{86}$$ $$\mathstrut -\mathstrut 3204q^{87}$$ $$\mathstrut -\mathstrut 72q^{88}$$ $$\mathstrut -\mathstrut 3084q^{89}$$ $$\mathstrut -\mathstrut 432q^{90}$$ $$\mathstrut +\mathstrut 2508q^{91}$$ $$\mathstrut -\mathstrut 1056q^{92}$$ $$\mathstrut -\mathstrut 2634q^{93}$$ $$\mathstrut +\mathstrut 612q^{94}$$ $$\mathstrut -\mathstrut 2016q^{95}$$ $$\mathstrut +\mathstrut 384q^{96}$$ $$\mathstrut +\mathstrut 1029q^{97}$$ $$\mathstrut +\mathstrut 2604q^{98}$$ $$\mathstrut +\mathstrut 1152q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

Decomposition of $$S_{4}^{\mathrm{new}}(18, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
18.4.c.a $$2$$ $$1.062$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$9$$ $$31$$ $$q-2\zeta_{6}q^{2}+(3-6\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$$
18.4.c.b $$4$$ $$1.062$$ $$\Q(\sqrt{-3}, \sqrt{-35})$$ None $$4$$ $$3$$ $$9$$ $$-19$$ $$q-2\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-4-4\beta _{1}+\cdots)q^{4}+\cdots$$

Decomposition of $$S_{4}^{\mathrm{old}}(18, [\chi])$$ into lower level spaces

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