# Properties

 Label 74.4.b Level $74$ Weight $4$ Character orbit 74.b Rep. character $\chi_{74}(73,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $1$ Sturm bound $38$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$74 = 2 \cdot 37$$ Weight: $$k$$ $$=$$ $$4$$ 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: $$38$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(74, [\chi])$$.

Total New Old
Modular forms 30 10 20
Cusp forms 26 10 16
Eisenstein series 4 0 4

## Trace form

 $$10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9} + O(q^{10})$$ $$10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9} + 76 q^{10} - 50 q^{11} - 56 q^{12} + 160 q^{16} - 312 q^{21} - 700 q^{25} + 492 q^{26} + 848 q^{27} + 16 q^{28} - 240 q^{30} - 508 q^{33} - 568 q^{34} - 688 q^{36} + 82 q^{37} + 336 q^{38} - 304 q^{40} - 1194 q^{41} + 200 q^{44} + 60 q^{46} + 464 q^{47} + 224 q^{48} + 2382 q^{49} - 692 q^{53} + 1108 q^{58} - 1700 q^{62} + 2300 q^{63} - 640 q^{64} + 604 q^{65} + 1114 q^{67} + 1880 q^{70} - 1460 q^{71} + 2082 q^{73} + 968 q^{74} - 5160 q^{75} - 6096 q^{77} + 1004 q^{78} + 4978 q^{81} - 1364 q^{83} + 1248 q^{84} + 104 q^{85} + 1400 q^{86} - 2600 q^{90} + 5084 q^{95} + 508 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(74, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
74.4.b.a $10$ $4.366$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$14$$ $$0$$ $$-4$$ $$q-\beta _{5}q^{2}+(1-\beta _{2})q^{3}-4q^{4}+(2\beta _{5}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(74, [\chi])$$ into lower level spaces

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