Properties

Label 43.9.b
Level $43$
Weight $9$
Character orbit 43.b
Rep. character $\chi_{43}(42,\cdot)$
Character field $\Q$
Dimension $29$
Newform subspaces $2$
Sturm bound $33$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(33\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(43, [\chi])\).

Total New Old
Modular forms 31 31 0
Cusp forms 29 29 0
Eisenstein series 2 2 0

Trace form

\( 29q - 4028q^{4} - 1794q^{6} - 74193q^{9} + O(q^{10}) \) \( 29q - 4028q^{4} - 1794q^{6} - 74193q^{9} + 24982q^{10} + 14857q^{11} - 32635q^{13} + 24732q^{14} + 15388q^{15} + 591348q^{16} - 55169q^{17} - 261352q^{21} + 356287q^{23} + 1770326q^{24} - 2249809q^{25} + 479407q^{31} + 10947816q^{35} + 13281682q^{36} - 7189158q^{38} - 21389338q^{40} - 960905q^{41} + 5892221q^{43} - 6176816q^{44} - 5000240q^{47} - 9796135q^{49} - 1080700q^{52} + 10880833q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 13418942q^{59} - 44902072q^{60} - 153667356q^{64} - 48457584q^{66} - 170770235q^{67} + 170492674q^{68} + 205870278q^{74} + 267860612q^{78} + 80425884q^{79} - 14554283q^{81} - 135695411q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 271107950q^{92} + 123322986q^{95} - 692987086q^{96} - 156101641q^{97} - 542004247q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(43, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
43.9.b.a \(1\) \(17.517\) \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) \(q+2^{8}q^{4}+3^{8}q^{9}+10319q^{11}-54721q^{13}+\cdots\)
43.9.b.b \(28\) \(17.517\) None \(0\) \(0\) \(0\) \(0\)