# Properties

 Label 74.2.b Level $74$ Weight $2$ Character orbit 74.b Rep. character $\chi_{74}(73,\cdot)$ Character field $\Q$ Dimension $4$ 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.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$37$$ Character field: $$\Q$$ 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 12 4 8
Cusp forms 8 4 4
Eisenstein series 4 0 4

## Trace form

 $$4 q - 2 q^{3} - 4 q^{4} - 8 q^{7} + 10 q^{9} + O(q^{10})$$ $$4 q - 2 q^{3} - 4 q^{4} - 8 q^{7} + 10 q^{9} - 6 q^{10} + 6 q^{11} + 2 q^{12} + 4 q^{16} + 4 q^{21} - 10 q^{25} - 6 q^{26} - 20 q^{27} + 8 q^{28} + 24 q^{30} - 24 q^{33} + 12 q^{34} - 10 q^{36} + 16 q^{37} - 12 q^{38} + 6 q^{40} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 12 q^{47} - 2 q^{48} - 12 q^{49} + 12 q^{53} + 6 q^{58} - 6 q^{62} - 20 q^{63} - 4 q^{64} + 12 q^{65} - 2 q^{67} + 12 q^{70} + 10 q^{73} + 68 q^{75} - 12 q^{77} - 18 q^{78} - 20 q^{81} + 24 q^{83} - 4 q^{84} - 24 q^{85} - 24 q^{86} - 36 q^{90} - 60 q^{95} + 36 q^{99} + O(q^{100})$$

## 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.b.a $4$ $0.591$ $$\Q(i, \sqrt{21})$$ None $$0$$ $$-2$$ $$0$$ $$-8$$ $$q+\beta _{2}q^{2}+(-1+\beta _{3})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$

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

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