# Properties

 Label 592.2.bq Level $592$ Weight $2$ Character orbit 592.bq Rep. character $\chi_{592}(65,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $108$ Newform subspaces $5$ Sturm bound $152$ Trace bound $3$

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## Defining parameters

 Level: $$N$$ $$=$$ $$592 = 2^{4} \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 592.bq (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$37$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$5$$ Sturm bound: $$152$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(592, [\chi])$$.

Total New Old
Modular forms 492 120 372
Cusp forms 420 108 312
Eisenstein series 72 12 60

## Trace form

 $$108 q + 6 q^{3} - 9 q^{5} - 6 q^{9} + O(q^{10})$$ $$108 q + 6 q^{3} - 9 q^{5} - 6 q^{9} + 21 q^{11} - 6 q^{13} - 12 q^{15} - 9 q^{17} + 6 q^{19} - 6 q^{21} + 9 q^{23} - 3 q^{25} + 45 q^{27} - 9 q^{29} + 3 q^{33} + 6 q^{35} + 18 q^{37} + 12 q^{39} - 9 q^{41} - 9 q^{45} + 33 q^{47} + 6 q^{49} - 81 q^{51} - 18 q^{53} - 9 q^{55} - 6 q^{57} + 6 q^{59} - 36 q^{61} + 33 q^{63} + 3 q^{65} - 15 q^{69} + 24 q^{71} - 42 q^{73} + 96 q^{75} + 27 q^{77} - 66 q^{79} + 3 q^{81} + 36 q^{83} - 18 q^{85} - 27 q^{87} + 36 q^{89} + 48 q^{91} - 12 q^{93} + 6 q^{95} - 9 q^{97} - 141 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(592, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
592.2.bq.a $6$ $4.727$ $$\Q(\zeta_{18})$$ None $$0$$ $$-9$$ $$0$$ $$-3$$ $$q+(-1+\zeta_{18}^{2}-\zeta_{18}^{3}-\zeta_{18}^{4}-2\zeta_{18}^{5})q^{3}+\cdots$$
592.2.bq.b $12$ $4.727$ $$\Q(\zeta_{36})$$ None $$0$$ $$-6$$ $$0$$ $$12$$ $$q+(\zeta_{36}-\zeta_{36}^{3}-\zeta_{36}^{5})q^{3}+(-\zeta_{36}^{2}+\cdots)q^{5}+\cdots$$
592.2.bq.c $12$ $4.727$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$12$$ $$0$$ $$-6$$ $$q+(1-\beta _{1}+\beta _{6})q^{3}+(\beta _{4}+\beta _{10})q^{5}+\cdots$$
592.2.bq.d $18$ $4.727$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None $$0$$ $$9$$ $$-3$$ $$3$$ $$q+(1+\beta _{12}-\beta _{16})q^{3}+(-1-\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots$$
592.2.bq.e $60$ $4.727$ None $$0$$ $$0$$ $$-6$$ $$-6$$

## Decomposition of $$S_{2}^{\mathrm{old}}(592, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(592, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(37, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(74, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(148, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(296, [\chi])$$$$^{\oplus 2}$$