# Properties

 Label 74.2.a Level $74$ Weight $2$ Character orbit 74.a Rep. character $\chi_{74}(1,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $19$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$74 = 2 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 74.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$19$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(74))$$.

Total New Old
Modular forms 11 4 7
Cusp forms 8 4 4
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$2$$$$37$$FrickeDim
$$+$$$$-$$$-$$$2$$
$$-$$$$+$$$-$$$2$$
Plus space$$+$$$$0$$
Minus space$$-$$$$4$$

## Trace form

 $$4 q + 2 q^{3} + 4 q^{4} - 4 q^{6} + 2 q^{9} + O(q^{10})$$ $$4 q + 2 q^{3} + 4 q^{4} - 4 q^{6} + 2 q^{9} + 2 q^{10} - 6 q^{11} + 2 q^{12} - 4 q^{14} - 16 q^{15} + 4 q^{16} - 12 q^{17} - 8 q^{18} + 4 q^{19} - 4 q^{21} - 4 q^{22} - 4 q^{23} - 4 q^{24} + 10 q^{25} + 2 q^{26} + 20 q^{27} + 20 q^{31} - 8 q^{33} + 12 q^{34} - 4 q^{35} + 2 q^{36} - 4 q^{38} + 12 q^{39} + 2 q^{40} + 26 q^{41} + 16 q^{42} - 12 q^{43} - 6 q^{44} - 16 q^{45} + 2 q^{46} + 4 q^{47} + 2 q^{48} + 12 q^{49} + 16 q^{50} - 8 q^{51} - 20 q^{53} - 16 q^{54} + 12 q^{55} - 4 q^{56} - 4 q^{57} - 6 q^{58} - 16 q^{60} + 16 q^{61} + 14 q^{62} - 36 q^{63} + 4 q^{64} - 28 q^{65} + 8 q^{66} + 2 q^{67} - 12 q^{68} + 8 q^{69} - 28 q^{70} - 8 q^{72} - 18 q^{73} - 4 q^{74} - 12 q^{75} + 4 q^{76} + 12 q^{77} + 2 q^{78} - 4 q^{79} + 36 q^{81} + 8 q^{82} - 4 q^{84} - 24 q^{85} + 4 q^{87} - 4 q^{88} - 16 q^{89} + 28 q^{90} - 4 q^{92} - 8 q^{93} + 28 q^{95} - 4 q^{96} + 4 q^{97} - 16 q^{98} - 12 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(74))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 37
74.2.a.a $2$ $0.591$ $$\Q(\sqrt{13})$$ None $$-2$$ $$3$$ $$-1$$ $$2$$ $+$ $-$ $$q-q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots$$
74.2.a.b $2$ $0.591$ $$\Q(\sqrt{5})$$ None $$2$$ $$-1$$ $$1$$ $$-2$$ $-$ $+$ $$q+q^{2}-\beta q^{3}+q^{4}+(-1+3\beta )q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(74))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(74)) \simeq$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(37))$$$$^{\oplus 2}$$