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 $1$

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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

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

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 43
43.6.a.a 43.a 1.a $8$ $6.897$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-12\) \(-26\) \(-212\) \(-136\) $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(-2-\beta _{1}+\beta _{4}-\beta _{7})q^{3}+\cdots\)
43.6.a.b 43.a 1.a $10$ $6.897$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(8\) \(28\) \(138\) \(60\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(3+\beta _{6})q^{3}+(21-\beta _{1}+\cdots)q^{4}+\cdots\)