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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 $1$

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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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(43))\) 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
43.4.a.a 43.a 1.a $4$ $2.537$ 4.4.45868.1 None \(-4\) \(-11\) \(-27\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{2}+(-3+\beta _{2}-\beta _{3})q^{3}+\cdots\)
43.4.a.b 43.a 1.a $6$ $2.537$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(6\) \(7\) \(43\) \(8\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{3})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)