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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 239
239.4.a.a 239.a 1.a $22$ $14.101$ None \(-4\) \(-13\) \(-37\) \(-52\) $-$ $\mathrm{SU}(2)$
239.4.a.b 239.a 1.a $37$ $14.101$ None \(4\) \(11\) \(43\) \(60\) $+$ $\mathrm{SU}(2)$