# Properties

 Label 726.2.e Level $726$ Weight $2$ Character orbit 726.e Rep. character $\chi_{726}(487,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $72$ Newform subspaces $18$ Sturm bound $264$ Trace bound $10$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$726 = 2 \cdot 3 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 726.e (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$18$$ Sturm bound: $$264$$ Trace bound: $$10$$ Distinguishing $$T_p$$: $$5$$, $$7$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(726, [\chi])$$.

Total New Old
Modular forms 624 72 552
Cusp forms 432 72 360
Eisenstein series 192 0 192

## Trace form

 $$72q - 18q^{4} - 8q^{5} - 2q^{6} + 8q^{7} - 18q^{9} + O(q^{10})$$ $$72q - 18q^{4} - 8q^{5} - 2q^{6} + 8q^{7} - 18q^{9} + 12q^{10} + 4q^{14} - 2q^{15} - 18q^{16} + 16q^{17} - 20q^{19} - 8q^{20} + 16q^{21} + 16q^{23} - 2q^{24} - 6q^{25} - 16q^{26} - 2q^{28} + 12q^{29} - 12q^{30} - 6q^{31} + 24q^{34} - 28q^{35} - 18q^{36} - 28q^{37} - 16q^{38} - 8q^{39} + 2q^{40} - 20q^{41} - 2q^{42} + 32q^{43} - 8q^{45} - 12q^{46} - 46q^{49} + 24q^{50} + 12q^{51} + 4q^{53} + 8q^{54} - 16q^{56} + 12q^{57} - 18q^{58} + 4q^{59} + 8q^{60} + 4q^{61} + 12q^{62} + 8q^{63} - 18q^{64} + 8q^{65} + 64q^{67} + 16q^{68} - 12q^{69} + 14q^{70} + 6q^{73} + 16q^{74} - 32q^{75} + 20q^{79} + 12q^{80} - 18q^{81} - 24q^{82} - 28q^{83} - 4q^{84} + 24q^{85} + 12q^{86} - 20q^{87} + 32q^{89} - 8q^{90} + 40q^{91} - 24q^{92} + 60q^{93} - 16q^{94} - 52q^{95} - 2q^{96} + 44q^{97} - 48q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(726, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
726.2.e.a $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$-1$$ $$-5$$ $$-3$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
726.2.e.b $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$-1$$ $$0$$ $$2$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
726.2.e.c $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$-1$$ $$0$$ $$2$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
726.2.e.d $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$-1$$ $$1$$ $$-4$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
726.2.e.e $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$-1$$ $$4$$ $$2$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
726.2.e.f $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$1$$ $$-7$$ $$-1$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
726.2.e.g $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$1$$ $$-2$$ $$4$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
726.2.e.h $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$1$$ $$0$$ $$0$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
726.2.e.i $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$1$$ $$1$$ $$4$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
726.2.e.j $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$1$$ $$-1$$ $$-5$$ $$3$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots$$
726.2.e.k $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$1$$ $$-1$$ $$0$$ $$-2$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots$$
726.2.e.l $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$1$$ $$-1$$ $$1$$ $$4$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots$$
726.2.e.m $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$1$$ $$-1$$ $$4$$ $$-2$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots$$
726.2.e.n $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$1$$ $$1$$ $$-7$$ $$1$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots$$
726.2.e.o $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$1$$ $$1$$ $$-2$$ $$-4$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots$$
726.2.e.p $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$1$$ $$1$$ $$0$$ $$0$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots$$
726.2.e.q $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$1$$ $$1$$ $$1$$ $$-4$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots$$
726.2.e.r $$4$$ $$5.797$$ $$\Q(\zeta_{10})$$ None $$1$$ $$1$$ $$8$$ $$6$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(726, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(726, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(22, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(66, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(121, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(242, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(363, [\chi])$$$$^{\oplus 2}$$