# Properties

 Label 74.8.b Level $74$ Weight $8$ Character orbit 74.b Rep. character $\chi_{74}(73,\cdot)$ Character field $\Q$ Dimension $24$ Newform subspaces $1$ Sturm bound $76$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$74 = 2 \cdot 37$$ Weight: $$k$$ $$=$$ $$8$$ 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: $$76$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(74, [\chi])$$.

Total New Old
Modular forms 68 24 44
Cusp forms 64 24 40
Eisenstein series 4 0 4

## Trace form

 $$24 q - 106 q^{3} - 1536 q^{4} + 104 q^{7} + 17554 q^{9} + O(q^{10})$$ $$24 q - 106 q^{3} - 1536 q^{4} + 104 q^{7} + 17554 q^{9} + 1136 q^{10} + 366 q^{11} + 6784 q^{12} + 98304 q^{16} - 239820 q^{21} - 675570 q^{25} + 97008 q^{26} + 338780 q^{27} - 6656 q^{28} + 350400 q^{30} - 763792 q^{33} + 713632 q^{34} - 1123456 q^{36} + 41652 q^{37} - 30816 q^{38} - 72704 q^{40} + 1729722 q^{41} - 23424 q^{44} - 488496 q^{46} + 114756 q^{47} - 434176 q^{48} + 4003056 q^{49} - 1115964 q^{53} - 2075632 q^{58} + 3248208 q^{62} - 2350900 q^{63} - 6291456 q^{64} - 5246556 q^{65} - 2717994 q^{67} - 5649440 q^{70} + 10643280 q^{71} - 10450370 q^{73} - 1064064 q^{74} - 17737980 q^{75} + 11665236 q^{77} + 8431856 q^{78} + 47300176 q^{81} + 555912 q^{83} + 15348480 q^{84} - 4853096 q^{85} - 12070464 q^{86} + 32064160 q^{90} - 58516956 q^{95} - 53279900 q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(74, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
74.8.b.a $24$ $23.116$ None $$0$$ $$-106$$ $$0$$ $$104$$

## Decomposition of $$S_{8}^{\mathrm{old}}(74, [\chi])$$ into lower level spaces

$$S_{8}^{\mathrm{old}}(74, [\chi]) \simeq$$ $$S_{8}^{\mathrm{new}}(37, [\chi])$$$$^{\oplus 2}$$