# Properties

 Label 74.2.h Level $74$ Weight $2$ Character orbit 74.h Rep. character $\chi_{74}(3,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $12$ Newform subspaces $1$ Sturm bound $19$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$74 = 2 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 74.h (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$37$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$1$$ Sturm bound: $$19$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(74, [\chi])$$.

Total New Old
Modular forms 72 12 60
Cusp forms 48 12 36
Eisenstein series 24 0 24

## Trace form

 $$12 q + 6 q^{3} - 12 q^{7} - 6 q^{9} + O(q^{10})$$ $$12 q + 6 q^{3} - 12 q^{7} - 6 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 18 q^{14} - 18 q^{19} - 6 q^{21} - 18 q^{25} + 12 q^{26} - 6 q^{27} - 6 q^{28} + 18 q^{29} + 24 q^{30} - 6 q^{33} + 12 q^{34} + 18 q^{35} + 12 q^{36} + 30 q^{37} - 24 q^{38} + 30 q^{39} + 12 q^{40} + 24 q^{41} + 6 q^{44} - 18 q^{45} + 30 q^{46} + 6 q^{47} + 12 q^{49} - 36 q^{50} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 36 q^{57} + 6 q^{58} - 36 q^{61} - 6 q^{63} + 6 q^{64} + 36 q^{65} - 30 q^{67} - 18 q^{69} - 12 q^{70} + 12 q^{71} - 48 q^{74} - 36 q^{75} - 18 q^{76} + 12 q^{77} - 6 q^{78} + 6 q^{79} + 24 q^{81} - 48 q^{83} + 12 q^{84} + 18 q^{85} - 36 q^{86} + 36 q^{87} - 36 q^{88} - 18 q^{89} + 6 q^{90} - 6 q^{91} + 18 q^{92} - 12 q^{93} + 36 q^{97} + 36 q^{98} + 30 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(74, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
74.2.h.a $12$ $0.591$ $$\Q(\zeta_{36})$$ None $$0$$ $$6$$ $$0$$ $$-12$$ $$q+\zeta_{36}q^{2}+(1-\zeta_{36}^{4}-\zeta_{36}^{6})q^{3}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(74, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(74, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(37, [\chi])$$$$^{\oplus 2}$$