# Properties

 Label 43.4.a Level $43$ Weight $4$ Character orbit 43.a Rep. character $\chi_{43}(1,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $2$ Sturm bound $14$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$43$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 43.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$14$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_0(43))$$.

Total New Old
Modular forms 12 10 2
Cusp forms 10 10 0
Eisenstein series 2 0 2

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

$$43$$Dim.
$$+$$$$6$$
$$-$$$$4$$

## Trace form

 $$10q + 2q^{2} - 4q^{3} + 24q^{4} + 16q^{5} - 30q^{6} - 12q^{7} - 12q^{8} + 72q^{9} + O(q^{10})$$ $$10q + 2q^{2} - 4q^{3} + 24q^{4} + 16q^{5} - 30q^{6} - 12q^{7} - 12q^{8} + 72q^{9} + 54q^{10} - 90q^{11} - 96q^{12} + 54q^{13} - 72q^{14} - 32q^{15} + 148q^{16} - 188q^{17} + 218q^{18} + 24q^{19} + 216q^{20} - 108q^{21} - 302q^{22} + 28q^{23} - 358q^{24} + 4q^{25} - 6q^{26} + 20q^{27} - 484q^{28} + 416q^{29} - 96q^{30} + 368q^{31} + 216q^{32} + 508q^{33} - 54q^{34} - 176q^{35} - 306q^{36} - 180q^{37} - 82q^{38} + 388q^{39} + 746q^{40} - 20q^{41} - 32q^{42} - 86q^{43} - 1192q^{44} - 4q^{45} + 994q^{46} + 434q^{47} - 752q^{48} + 586q^{49} + 1934q^{50} + 408q^{51} + 216q^{52} - 770q^{53} + 80q^{54} - 372q^{55} - 436q^{56} - 768q^{57} - 1826q^{58} + 1172q^{59} - 2888q^{60} - 956q^{61} + 1506q^{62} - 376q^{63} + 900q^{64} - 412q^{65} + 968q^{66} - 522q^{67} - 1126q^{68} - 2368q^{69} - 2620q^{70} + 324q^{71} + 252q^{72} + 1492q^{73} + 1602q^{74} - 2432q^{75} + 2676q^{76} + 616q^{77} + 2132q^{78} - 518q^{79} + 2368q^{80} + 1954q^{81} - 614q^{82} - 1662q^{83} + 3148q^{84} - 68q^{85} - 430q^{86} - 58q^{87} + 1208q^{88} + 2640q^{89} - 1468q^{90} - 3048q^{91} + 974q^{92} + 1844q^{93} + 964q^{94} + 1070q^{95} - 2142q^{96} - 1820q^{97} + 4050q^{98} - 1670q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_0(43))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 43
43.4.a.a $$4$$ $$2.537$$ 4.4.45868.1 None $$-4$$ $$-11$$ $$-27$$ $$-20$$ $$-$$ $$q+(-1+\beta _{3})q^{2}+(-3+\beta _{2}-\beta _{3})q^{3}+\cdots$$
43.4.a.b $$6$$ $$2.537$$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$6$$ $$7$$ $$43$$ $$8$$ $$+$$ $$q+(1-\beta _{1})q^{2}+(1-\beta _{3})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots$$