# Properties

 Label 58.2.d Level $58$ Weight $2$ Character orbit 58.d Rep. character $\chi_{58}(7,\cdot)$ Character field $\Q(\zeta_{7})$ Dimension $18$ Newform subspaces $2$ Sturm bound $15$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$58 = 2 \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 58.d (of order $$7$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$29$$ Character field: $$\Q(\zeta_{7})$$ Newform subspaces: $$2$$ Sturm bound: $$15$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 54 18 36
Cusp forms 30 18 12
Eisenstein series 24 0 24

## Trace form

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

## 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.d.a $6$ $0.463$ $$\Q(\zeta_{14})$$ None $$1$$ $$3$$ $$-4$$ $$-5$$ $$q-\zeta_{14}^{4}q^{2}+(1-\zeta_{14}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{3}+\cdots$$
58.2.d.b $12$ $0.463$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-2$$ $$-3$$ $$0$$ $$1$$ $$q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{6}q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$$

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

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