# Properties

 Label 441.2.z Level $441$ Weight $2$ Character orbit 441.z Rep. character $\chi_{441}(4,\cdot)$ Character field $\Q(\zeta_{21})$ Dimension $648$ Newform subspaces $1$ Sturm bound $112$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 441.z (of order $$21$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$441$$ Character field: $$\Q(\zeta_{21})$$ Newform subspaces: $$1$$ Sturm bound: $$112$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(441, [\chi])$$.

Total New Old
Modular forms 696 696 0
Cusp forms 648 648 0
Eisenstein series 48 48 0

## Trace form

 $$648q - 8q^{2} - 13q^{3} + 44q^{4} + 3q^{5} + 2q^{6} - 7q^{7} - 16q^{8} - 39q^{9} + O(q^{10})$$ $$648q - 8q^{2} - 13q^{3} + 44q^{4} + 3q^{5} + 2q^{6} - 7q^{7} - 16q^{8} - 39q^{9} - 22q^{10} - 5q^{11} + 2q^{12} - 4q^{13} + 52q^{14} - 4q^{15} + 38q^{16} - 37q^{17} - 16q^{18} - 14q^{19} - 11q^{20} - 6q^{21} - q^{22} - 20q^{23} - 26q^{24} - 97q^{25} - 44q^{26} + 14q^{27} - 22q^{28} - 53q^{29} - 9q^{30} + 10q^{31} - 10q^{32} + 2q^{33} - 7q^{34} - 32q^{35} - 22q^{36} - 39q^{37} + 59q^{38} - 26q^{39} - 19q^{40} - 17q^{41} - 83q^{42} - q^{43} - 31q^{44} + 81q^{45} + 56q^{46} + 50q^{47} - 23q^{48} - 19q^{49} - 21q^{50} - 30q^{51} - 9q^{52} + 50q^{53} + 48q^{54} + 20q^{55} - 239q^{56} + 33q^{57} + 17q^{58} - 37q^{59} - 152q^{60} - 105q^{61} - 30q^{62} + 6q^{63} - 88q^{64} - 5q^{65} - 99q^{66} + 13q^{67} - 290q^{68} + 64q^{69} + 17q^{70} - 19q^{71} + 11q^{72} - 40q^{73} - 57q^{74} + 69q^{75} - 41q^{76} + 19q^{77} + 81q^{78} + 13q^{79} + 163q^{80} - 179q^{81} - 28q^{82} + 73q^{83} - 341q^{84} - 10q^{85} + 15q^{86} + 13q^{87} - 13q^{88} - 104q^{89} + 171q^{90} - 49q^{91} - 91q^{92} - 275q^{93} - 4q^{94} - 29q^{95} + 231q^{96} - 11q^{97} - 33q^{98} + 62q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(441, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
441.2.z.a $$648$$ $$3.521$$ None $$-8$$ $$-13$$ $$3$$ $$-7$$