# Properties

 Label 55.2.g Level $55$ Weight $2$ Character orbit 55.g Rep. character $\chi_{55}(16,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $16$ Newform subspaces $2$ Sturm bound $12$ Trace bound $2$

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## Defining parameters

 Level: $$N$$ $$=$$ $$55 = 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 55.g (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$2$$ Sturm bound: $$12$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(55, [\chi])$$.

Total New Old
Modular forms 32 16 16
Cusp forms 16 16 0
Eisenstein series 16 0 16

## Trace form

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

## Decomposition of $$S_{2}^{\mathrm{new}}(55, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
55.2.g.a $8$ $0.439$ 8.0.159390625.1 None $$-4$$ $$1$$ $$-2$$ $$-3$$ $$q+(-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots$$
55.2.g.b $8$ $0.439$ 8.0.13140625.1 None $$-2$$ $$-5$$ $$2$$ $$-1$$ $$q-\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$$