Properties

Label 43.8.a
Level $43$
Weight $8$
Character orbit 43.a
Rep. character $\chi_{43}(1,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $2$
Sturm bound $29$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 43.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(29\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(43))\).

Total New Old
Modular forms 26 24 2
Cusp forms 24 24 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.
\(+\)\(13\)
\(-\)\(11\)

Trace form

\( 24q - 8q^{2} + 26q^{3} + 1524q^{4} + 246q^{5} - 498q^{6} + 1348q^{7} + 60q^{8} + 12732q^{9} + O(q^{10}) \) \( 24q - 8q^{2} + 26q^{3} + 1524q^{4} + 246q^{5} - 498q^{6} + 1348q^{7} + 60q^{8} + 12732q^{9} + 3334q^{10} + 2953q^{11} - 14592q^{12} - 4417q^{13} + 21808q^{14} - 18092q^{15} + 79620q^{16} + 47785q^{17} - 6664q^{18} + 50534q^{19} - 113744q^{20} - 9948q^{21} - 87854q^{22} + 22045q^{23} - 268294q^{24} + 273604q^{25} + 139158q^{26} + 12188q^{27} + 195468q^{28} - 23112q^{29} + 528864q^{30} - 309139q^{31} - 444808q^{32} + 628282q^{33} + 681494q^{34} - 765996q^{35} - 182814q^{36} - 122434q^{37} + 282458q^{38} - 502382q^{39} + 1737786q^{40} - 1756995q^{41} - 2239952q^{42} - 159014q^{43} + 957216q^{44} + 842606q^{45} - 387654q^{46} + 74728q^{47} + 3287056q^{48} + 983204q^{49} - 1014056q^{50} - 1117314q^{51} - 3189224q^{52} + 1781963q^{53} - 3648928q^{54} - 1448112q^{55} + 1089580q^{56} - 4354596q^{57} + 345062q^{58} - 3575380q^{59} - 5800808q^{60} + 1757360q^{61} + 1888106q^{62} + 5381804q^{63} + 1661220q^{64} + 3437548q^{65} - 2433544q^{66} - 8853161q^{67} - 69870q^{68} + 3326210q^{69} - 260020q^{70} - 5748490q^{71} + 12570180q^{72} + 3767916q^{73} - 2566926q^{74} + 23766478q^{75} + 16548388q^{76} + 242076q^{77} - 13227508q^{78} - 8595612q^{79} + 141888q^{80} + 22136488q^{81} + 19725206q^{82} + 11790561q^{83} - 1661828q^{84} - 13047508q^{85} - 3180280q^{86} - 9567520q^{87} - 13260888q^{88} - 4240054q^{89} + 23700392q^{90} + 5834660q^{91} - 40411298q^{92} + 4027370q^{93} - 4356948q^{94} + 18458840q^{95} - 36415758q^{96} - 998049q^{97} - 2395688q^{98} + 34451509q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(43))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 43
43.8.a.a \(11\) \(13.433\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-24\) \(-68\) \(-752\) \(-12\) \(-\) \(q+(-2-\beta _{1})q^{2}+(-6-\beta _{5})q^{3}+(54+\cdots)q^{4}+\cdots\)
43.8.a.b \(13\) \(13.433\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(16\) \(94\) \(998\) \(1360\) \(+\) \(q+(1+\beta _{1})q^{2}+(7+\beta _{3})q^{3}+(71+2\beta _{1}+\cdots)q^{4}+\cdots\)