# Properties

 Label 726.2.i Level $726$ Weight $2$ Character orbit 726.i Rep. character $\chi_{726}(67,\cdot)$ Character field $\Q(\zeta_{11})$ Dimension $220$ Newform subspaces $4$ Sturm bound $264$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$726 = 2 \cdot 3 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 726.i (of order $$11$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$121$$ Character field: $$\Q(\zeta_{11})$$ Newform subspaces: $$4$$ Sturm bound: $$264$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 1360 220 1140
Cusp forms 1280 220 1060
Eisenstein series 80 0 80

## Trace form

 $$220q - 22q^{4} + 8q^{5} + 2q^{6} + 12q^{7} + 220q^{9} + O(q^{10})$$ $$220q - 22q^{4} + 8q^{5} + 2q^{6} + 12q^{7} + 220q^{9} - 14q^{10} - 32q^{11} - 68q^{13} - 28q^{14} + 12q^{15} - 22q^{16} + 24q^{17} + 20q^{19} + 8q^{20} + 4q^{21} - 34q^{22} + 16q^{23} + 2q^{24} + 6q^{25} + 8q^{26} + 12q^{28} + 8q^{29} + 12q^{30} - 16q^{31} + 10q^{33} + 8q^{34} + 48q^{35} - 22q^{36} - 92q^{37} + 8q^{38} + 8q^{39} - 36q^{40} + 40q^{41} + 4q^{42} + 28q^{43} + 12q^{44} + 8q^{45} + 32q^{46} + 56q^{47} - 66q^{49} + 16q^{50} + 28q^{51} + 20q^{52} - 4q^{53} + 2q^{54} + 28q^{55} + 16q^{56} + 28q^{57} - 32q^{58} + 40q^{59} + 12q^{60} + 76q^{61} + 48q^{62} + 12q^{63} - 22q^{64} - 20q^{65} + 8q^{66} - 156q^{67} + 24q^{68} + 24q^{69} - 4q^{70} - 16q^{71} + 40q^{73} + 24q^{74} + 16q^{75} - 24q^{76} + 88q^{77} - 72q^{79} + 8q^{80} + 220q^{81} - 4q^{82} + 88q^{83} + 4q^{84} - 80q^{85} + 40q^{86} + 20q^{87} + 10q^{88} - 24q^{89} - 14q^{90} - 52q^{91} - 28q^{92} + 16q^{93} - 296q^{94} + 112q^{95} + 2q^{96} - 56q^{97} + 48q^{98} - 32q^{99} + O(q^{100})$$

## 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.i.a $$50$$ $$5.797$$ None $$-5$$ $$50$$ $$10$$ $$9$$
726.2.i.b $$50$$ $$5.797$$ None $$5$$ $$-50$$ $$0$$ $$-1$$
726.2.i.c $$60$$ $$5.797$$ None $$-6$$ $$-60$$ $$-2$$ $$5$$
726.2.i.d $$60$$ $$5.797$$ None $$6$$ $$60$$ $$0$$ $$-1$$

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

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