# Properties

 Label 43.6.a Level $43$ Weight $6$ Character orbit 43.a Rep. character $\chi_{43}(1,\cdot)$ Character field $\Q$ Dimension $18$ Newform subspaces $2$ Sturm bound $22$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$43$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 43.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$22$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_0(43))$$.

Total New Old
Modular forms 20 18 2
Cusp forms 18 18 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.
$$+$$$$8$$
$$-$$$$10$$

## Trace form

 $$18q - 4q^{2} + 2q^{3} + 324q^{4} - 74q^{5} + 6q^{6} - 76q^{7} - 372q^{8} + 1902q^{9} + O(q^{10})$$ $$18q - 4q^{2} + 2q^{3} + 324q^{4} - 74q^{5} + 6q^{6} - 76q^{7} - 372q^{8} + 1902q^{9} - 634q^{10} + 213q^{11} + 432q^{12} - 575q^{13} - 2304q^{14} - 92q^{15} + 7236q^{16} + 1483q^{17} - 6436q^{18} - 4082q^{19} - 1296q^{20} - 2484q^{21} + 5666q^{22} - 755q^{23} + 9242q^{24} + 11498q^{25} + 3102q^{26} - 11284q^{27} + 3612q^{28} + 2636q^{29} - 23328q^{30} + 805q^{31} - 25848q^{32} - 28586q^{33} + 2974q^{34} + 12724q^{35} + 72402q^{36} - 2306q^{37} + 7346q^{38} - 15422q^{39} - 78342q^{40} - 401q^{41} + 41056q^{42} + 3698q^{43} - 36496q^{44} + 28910q^{45} - 1398q^{46} - 29272q^{47} - 35120q^{48} + 36646q^{49} + 27860q^{50} + 12726q^{51} - 46504q^{52} + 64813q^{53} - 30976q^{54} + 57120q^{55} - 152308q^{56} + 33252q^{57} + 42646q^{58} + 73148q^{59} + 212872q^{60} - 65132q^{61} + 19242q^{62} - 59524q^{63} + 201060q^{64} + 49484q^{65} - 198808q^{66} + 25763q^{67} + 232658q^{68} - 92122q^{69} + 152716q^{70} + 1782q^{71} - 485052q^{72} + 64152q^{73} - 140670q^{74} + 122758q^{75} - 248524q^{76} - 119996q^{77} + 235676q^{78} + 68724q^{79} + 10960q^{80} + 134626q^{81} - 206690q^{82} - 182379q^{83} - 341300q^{84} + 53884q^{85} + 36980q^{86} + 449336q^{87} - 332280q^{88} - 328374q^{89} - 473680q^{90} + 105844q^{91} + 374174q^{92} - 362290q^{93} + 255996q^{94} - 169456q^{95} + 788418q^{96} + 253125q^{97} + 62412q^{98} - 30983q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_0(43))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 43
43.6.a.a $$8$$ $$6.897$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$-12$$ $$-26$$ $$-212$$ $$-136$$ $$+$$ $$q+(-2+\beta _{1})q^{2}+(-2-\beta _{1}+\beta _{4}-\beta _{7})q^{3}+\cdots$$
43.6.a.b $$10$$ $$6.897$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$8$$ $$28$$ $$138$$ $$60$$ $$-$$ $$q+(1-\beta _{1})q^{2}+(3+\beta _{6})q^{3}+(21-\beta _{1}+\cdots)q^{4}+\cdots$$