# Properties

 Label 43.2.a Level 43 Weight 2 Character orbit a Rep. character $$\chi_{43}(1,\cdot)$$ Character field $$\Q$$ Dimension 3 Newform subspaces 2 Sturm bound 7 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$43$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 43.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$7$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(43))$$.

Total New Old
Modular forms 4 4 0
Cusp forms 3 3 0
Eisenstein series 1 1 0

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.
$$+$$$$1$$
$$-$$$$2$$

## Trace form

 $$3q - 2q^{2} - 2q^{3} + 2q^{4} - 4q^{7} - q^{9} + O(q^{10})$$ $$3q - 2q^{2} - 2q^{3} + 2q^{4} - 4q^{7} - q^{9} + 4q^{10} + q^{11} - 4q^{12} - 3q^{13} + 4q^{14} + 12q^{15} - 12q^{16} + 7q^{17} - 2q^{18} - 6q^{19} - 8q^{20} - 4q^{21} + 2q^{22} + q^{23} + 8q^{24} + 13q^{25} + 18q^{26} + 4q^{27} - 6q^{29} - 24q^{30} - 7q^{31} + 8q^{32} - 14q^{33} + 14q^{34} - 12q^{35} + 2q^{36} - 4q^{38} + 2q^{39} + 8q^{40} + 3q^{41} + 8q^{42} + q^{43} + 6q^{44} - 8q^{45} - 14q^{46} + 16q^{47} + 8q^{48} - 9q^{49} - 38q^{50} - 2q^{51} - 10q^{52} + 17q^{53} + 8q^{54} - 24q^{55} - 8q^{56} + 12q^{57} + 24q^{58} - 16q^{59} + 16q^{60} + 10q^{61} + 2q^{62} + 4q^{63} + 8q^{64} + 16q^{65} + 16q^{66} - q^{67} - 6q^{68} + 18q^{69} + 16q^{70} - 10q^{71} - 22q^{73} - 24q^{74} - 6q^{75} - 4q^{76} + 12q^{77} - 24q^{78} - 4q^{79} - 21q^{81} - 18q^{82} + 33q^{83} + 24q^{85} + 2q^{86} - 16q^{88} - 16q^{89} + 12q^{90} + 4q^{91} - 2q^{92} + 2q^{93} - 8q^{94} + 8q^{95} - 16q^{96} + 5q^{97} - 2q^{98} + 5q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(43))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 43
43.2.a.a $$1$$ $$0.343$$ $$\Q$$ None $$-2$$ $$-2$$ $$-4$$ $$0$$ $$+$$ $$q-2q^{2}-2q^{3}+2q^{4}-4q^{5}+4q^{6}+\cdots$$
43.2.a.b $$2$$ $$0.343$$ $$\Q(\sqrt{2})$$ None $$0$$ $$0$$ $$4$$ $$-4$$ $$-$$ $$q+\beta q^{2}-\beta q^{3}+(2-\beta )q^{5}-2q^{6}+(-2+\cdots)q^{7}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + 2 T + 2 T^{2}$$)($$1 + 2 T^{2} + 4 T^{4}$$)
$3$ ($$1 + 2 T + 3 T^{2}$$)($$1 + 4 T^{2} + 9 T^{4}$$)
$5$ ($$1 + 4 T + 5 T^{2}$$)($$1 - 4 T + 12 T^{2} - 20 T^{3} + 25 T^{4}$$)
$7$ ($$1 + 7 T^{2}$$)($$1 + 4 T + 16 T^{2} + 28 T^{3} + 49 T^{4}$$)
$11$ ($$1 - 3 T + 11 T^{2}$$)($$1 + 2 T + 15 T^{2} + 22 T^{3} + 121 T^{4}$$)
$13$ ($$1 + 5 T + 13 T^{2}$$)($$1 - 2 T + 19 T^{2} - 26 T^{3} + 169 T^{4}$$)
$17$ ($$1 + 3 T + 17 T^{2}$$)($$1 - 10 T + 51 T^{2} - 170 T^{3} + 289 T^{4}$$)
$19$ ($$1 + 2 T + 19 T^{2}$$)($$1 + 4 T + 34 T^{2} + 76 T^{3} + 361 T^{4}$$)
$23$ ($$1 + T + 23 T^{2}$$)($$1 - 2 T + 15 T^{2} - 46 T^{3} + 529 T^{4}$$)
$29$ ($$1 + 6 T + 29 T^{2}$$)($$1 + 40 T^{2} + 841 T^{4}$$)
$31$ ($$1 + T + 31 T^{2}$$)($$( 1 + 3 T + 31 T^{2} )^{2}$$)
$37$ ($$1 + 37 T^{2}$$)($$1 + 2 T^{2} + 1369 T^{4}$$)
$41$ ($$1 - 5 T + 41 T^{2}$$)($$1 + 2 T + 75 T^{2} + 82 T^{3} + 1681 T^{4}$$)
$43$ ($$1 + T$$)($$( 1 - T )^{2}$$)
$47$ ($$1 - 4 T + 47 T^{2}$$)($$( 1 - 6 T + 47 T^{2} )^{2}$$)
$53$ ($$1 + 5 T + 53 T^{2}$$)($$1 - 22 T + 219 T^{2} - 1166 T^{3} + 2809 T^{4}$$)
$59$ ($$1 + 12 T + 59 T^{2}$$)($$1 + 4 T + 114 T^{2} + 236 T^{3} + 3481 T^{4}$$)
$61$ ($$1 - 2 T + 61 T^{2}$$)($$1 - 8 T + 120 T^{2} - 488 T^{3} + 3721 T^{4}$$)
$67$ ($$1 + 3 T + 67 T^{2}$$)($$1 - 2 T + 63 T^{2} - 134 T^{3} + 4489 T^{4}$$)
$71$ ($$1 - 2 T + 71 T^{2}$$)($$1 + 12 T + 170 T^{2} + 852 T^{3} + 5041 T^{4}$$)
$73$ ($$1 - 2 T + 73 T^{2}$$)($$1 + 24 T + 272 T^{2} + 1752 T^{3} + 5329 T^{4}$$)
$79$ ($$1 + 8 T + 79 T^{2}$$)($$1 - 4 T + 154 T^{2} - 316 T^{3} + 6241 T^{4}$$)
$83$ ($$1 - 15 T + 83 T^{2}$$)($$1 - 18 T + 215 T^{2} - 1494 T^{3} + 6889 T^{4}$$)
$89$ ($$1 + 4 T + 89 T^{2}$$)($$1 + 12 T + 196 T^{2} + 1068 T^{3} + 7921 T^{4}$$)
$97$ ($$1 - 7 T + 97 T^{2}$$)($$1 + 2 T + 187 T^{2} + 194 T^{3} + 9409 T^{4}$$)