# Properties

 Label 58.2.b Level $58$ Weight $2$ Character orbit 58.b Rep. character $\chi_{58}(57,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $15$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$58 = 2 \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 58.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$29$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$15$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(58, [\chi])$$.

Total New Old
Modular forms 10 2 8
Cusp forms 6 2 4
Eisenstein series 4 0 4

## Trace form

 $$2 q - 2 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{9} + O(q^{10})$$ $$2 q - 2 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{9} - 2 q^{13} + 2 q^{16} - 2 q^{20} + 10 q^{22} - 12 q^{23} + 2 q^{24} - 8 q^{25} + 4 q^{28} + 10 q^{29} - 2 q^{30} + 10 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36} - 8 q^{38} + 4 q^{42} + 4 q^{45} - 6 q^{49} + 4 q^{51} + 2 q^{52} - 2 q^{53} - 10 q^{54} - 8 q^{57} - 4 q^{58} + 20 q^{59} - 10 q^{62} - 8 q^{63} - 2 q^{64} - 2 q^{65} + 16 q^{67} - 16 q^{71} - 16 q^{74} + 2 q^{78} + 2 q^{80} + 2 q^{81} + 20 q^{82} + 28 q^{83} + 18 q^{86} - 4 q^{87} - 10 q^{88} + 4 q^{91} + 12 q^{92} - 10 q^{93} - 6 q^{94} - 2 q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(58, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
58.2.b.a $2$ $0.463$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$-4$$ $$q+iq^{2}+iq^{3}-q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(58, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(58, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(29, [\chi])$$$$^{\oplus 2}$$