Properties

 Label 441.2.bh Level $441$ Weight $2$ Character orbit 441.bh Rep. character $\chi_{441}(20,\cdot)$ Character field $\Q(\zeta_{42})$ Dimension $648$ Newform subspaces $1$ Sturm bound $112$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 441.bh (of order $$42$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$441$$ Character field: $$\Q(\zeta_{42})$$ 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

 $$648 q - 15 q^{2} - 14 q^{3} - 57 q^{4} - 21 q^{5} + 14 q^{6} - 5 q^{7} - 20 q^{9} + O(q^{10})$$ $$648 q - 15 q^{2} - 14 q^{3} - 57 q^{4} - 21 q^{5} + 14 q^{6} - 5 q^{7} - 20 q^{9} - 28 q^{10} - 15 q^{11} + 21 q^{12} - 7 q^{13} - 114 q^{14} - 10 q^{15} + 39 q^{16} - 18 q^{18} - 21 q^{20} + 10 q^{21} + 3 q^{22} + 30 q^{23} - 14 q^{24} + 41 q^{25} + 7 q^{27} - 20 q^{28} + 75 q^{29} - 70 q^{30} - 39 q^{32} - 14 q^{33} - 7 q^{34} - 128 q^{36} - 10 q^{37} + 21 q^{38} - 36 q^{39} - 7 q^{40} - 21 q^{41} + 104 q^{42} + 3 q^{43} - 35 q^{45} - 72 q^{46} - 147 q^{47} - 13 q^{49} - 18 q^{50} + 22 q^{51} - 35 q^{52} - 14 q^{54} - 112 q^{55} - 63 q^{56} - 16 q^{57} + 33 q^{58} - 21 q^{59} - 90 q^{60} - 56 q^{61} - 38 q^{63} + 52 q^{64} + 27 q^{65} - 42 q^{66} - 26 q^{67} - 182 q^{69} - 25 q^{70} + 24 q^{72} - 28 q^{73} + 33 q^{74} - 14 q^{75} + 21 q^{76} + 3 q^{77} + 90 q^{78} - 2 q^{79} + 56 q^{81} - 28 q^{82} - 21 q^{83} + 116 q^{84} + 5 q^{85} - 123 q^{86} - 70 q^{87} - 41 q^{88} - 224 q^{90} - 4 q^{91} - 225 q^{92} + 112 q^{93} - 7 q^{94} - 12 q^{95} - 371 q^{96} + 224 q^{99} + O(q^{100})$$

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.bh.a $$648$$ $$3.521$$ None $$-15$$ $$-14$$ $$-21$$ $$-5$$