Properties

Label 239.4.a
Level $239$
Weight $4$
Character orbit 239.a
Rep. character $\chi_{239}(1,\cdot)$
Character field $\Q$
Dimension $59$
Newform subspaces $2$
Sturm bound $80$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 239.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(239))\).

Total New Old
Modular forms 61 59 2
Cusp forms 59 59 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.

\(239\)Dim.
\(+\)\(37\)
\(-\)\(22\)

Trace form

\( 59q - 2q^{3} + 220q^{4} + 6q^{5} + 12q^{6} + 8q^{7} - 42q^{8} + 543q^{9} + O(q^{10}) \) \( 59q - 2q^{3} + 220q^{4} + 6q^{5} + 12q^{6} + 8q^{7} - 42q^{8} + 543q^{9} + 54q^{10} - 22q^{11} - 16q^{12} + 32q^{13} + 58q^{14} + 76q^{15} + 876q^{16} - 30q^{17} - 222q^{18} + 74q^{19} + 172q^{20} - 108q^{21} - 164q^{22} - 128q^{23} + 158q^{24} + 1333q^{25} + 340q^{26} + 376q^{27} + 314q^{28} + 82q^{29} + 114q^{30} + 106q^{31} - 646q^{32} + 408q^{33} + 126q^{34} - 160q^{35} + 2008q^{36} + 80q^{37} + 1086q^{38} + 8q^{39} + 192q^{40} + 330q^{41} + 1292q^{42} + 906q^{43} + 490q^{44} + 462q^{45} - 148q^{46} + 1112q^{47} + 270q^{48} + 2711q^{49} + 458q^{50} + 372q^{51} + 1110q^{52} + 324q^{53} + 912q^{54} - 380q^{55} + 1752q^{56} + 1352q^{57} + 240q^{58} + 130q^{59} + 2613q^{60} + 682q^{61} - 2313q^{62} - 780q^{63} + 4134q^{64} - 12q^{65} - 2745q^{66} + 846q^{67} - 4004q^{68} + 1148q^{69} - 2924q^{70} - 2914q^{71} - 7157q^{72} + 894q^{73} + 1398q^{74} - 2098q^{75} + 126q^{76} - 2156q^{77} - 3588q^{78} + 2656q^{79} - 2059q^{80} + 5283q^{81} - 4962q^{82} + 126q^{83} - 9698q^{84} + 1416q^{85} - 542q^{86} - 3728q^{87} - 740q^{88} - 498q^{89} - 1923q^{90} - 2012q^{91} - 7356q^{92} + 5192q^{93} - 810q^{94} + 976q^{95} - 8094q^{96} + 1202q^{97} + 906q^{98} - 3754q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(239))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 239
239.4.a.a \(22\) \(14.101\) None \(-4\) \(-13\) \(-37\) \(-52\) \(-\)
239.4.a.b \(37\) \(14.101\) None \(4\) \(11\) \(43\) \(60\) \(+\)