Properties

 Label 402.2.e Level 402 Weight 2 Character orbit e Rep. character $$\chi_{402}(37,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 24 Newforms 4 Sturm bound 136 Trace bound 3

Related objects

Defining parameters

 Level: $$N$$ = $$402 = 2 \cdot 3 \cdot 67$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 402.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$67$$ Character field: $$\Q(\zeta_{3})$$ Newforms: $$4$$ Sturm bound: $$136$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(402, [\chi])$$.

Total New Old
Modular forms 144 24 120
Cusp forms 128 24 104
Eisenstein series 16 0 16

Trace form

 $$24q - 12q^{4} + 24q^{9} + O(q^{10})$$ $$24q - 12q^{4} + 24q^{9} - 4q^{11} + 8q^{13} + 8q^{14} + 8q^{15} - 12q^{16} - 4q^{17} + 8q^{19} - 4q^{21} - 16q^{22} + 12q^{23} + 40q^{25} + 16q^{29} + 4q^{30} + 28q^{31} - 4q^{33} + 4q^{34} - 28q^{35} - 12q^{36} - 12q^{37} + 12q^{39} - 12q^{41} - 8q^{42} + 8q^{43} - 4q^{44} + 44q^{47} - 24q^{49} - 16q^{50} - 8q^{51} - 16q^{52} + 8q^{53} - 12q^{55} - 4q^{56} - 8q^{57} - 16q^{58} - 24q^{59} - 4q^{60} - 12q^{61} - 40q^{62} + 24q^{64} + 12q^{65} - 24q^{66} - 44q^{67} + 8q^{68} - 8q^{69} + 8q^{70} - 44q^{71} - 12q^{73} + 12q^{74} - 16q^{75} - 16q^{76} - 20q^{77} + 16q^{78} - 36q^{79} + 24q^{81} + 12q^{83} - 4q^{84} - 12q^{85} + 32q^{86} + 8q^{88} + 48q^{89} + 56q^{91} - 24q^{92} + 8q^{93} - 64q^{94} - 4q^{95} - 4q^{97} + 16q^{98} - 4q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(402, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
402.2.e.a $$6$$ $$3.210$$ 6.0.16638075.1 None $$-3$$ $$-6$$ $$0$$ $$-1$$ $$q+\beta _{4}q^{2}-q^{3}+(-1-\beta _{4})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$$
402.2.e.b $$6$$ $$3.210$$ 6.0.48843675.1 None $$-3$$ $$6$$ $$0$$ $$-1$$ $$q+(-1+\beta _{4})q^{2}+q^{3}-\beta _{4}q^{4}-\beta _{2}q^{5}+\cdots$$
402.2.e.c $$6$$ $$3.210$$ 6.0.309123.1 None $$3$$ $$-6$$ $$-4$$ $$3$$ $$q+\beta _{4}q^{2}-q^{3}+(-1+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots$$
402.2.e.d $$6$$ $$3.210$$ 6.0.18825075.4 None $$3$$ $$6$$ $$4$$ $$-1$$ $$q-\beta _{1}q^{2}+q^{3}+(-1-\beta _{1})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(402, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(402, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(67, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(134, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(201, [\chi])$$$$^{\oplus 2}$$