Properties

Label 63.4.g
Level $63$
Weight $4$
Character orbit 63.g
Rep. character $\chi_{63}(4,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $44$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(63, [\chi])\).

Total New Old
Modular forms 52 52 0
Cusp forms 44 44 0
Eisenstein series 8 8 0

Trace form

\( 44q + q^{2} - q^{3} - 79q^{4} + 38q^{5} - 20q^{6} - 7q^{7} - 24q^{8} - 31q^{9} + O(q^{10}) \) \( 44q + q^{2} - q^{3} - 79q^{4} + 38q^{5} - 20q^{6} - 7q^{7} - 24q^{8} - 31q^{9} - 18q^{10} - 10q^{11} - 41q^{12} - 14q^{13} - 79q^{14} + 119q^{15} - 247q^{16} - 162q^{17} + 157q^{18} + 58q^{19} - 362q^{20} + 166q^{21} - 18q^{22} + 186q^{23} + 414q^{24} + 698q^{25} - 266q^{26} + 272q^{27} - 172q^{28} + 248q^{29} + 616q^{30} + 61q^{31} - 163q^{32} + 23q^{33} + 6q^{34} + 289q^{35} - 806q^{36} - 86q^{37} + 1522q^{38} - 565q^{39} + 36q^{40} - 692q^{41} + 395q^{42} - 86q^{43} - 443q^{44} - 1483q^{45} - 270q^{46} - 1005q^{47} - 1013q^{48} - 277q^{49} + 239q^{50} - 1719q^{51} + 670q^{52} + 258q^{53} + 910q^{54} - 870q^{55} + 714q^{56} + 566q^{57} - 474q^{58} - 1665q^{59} + 4q^{60} + 439q^{61} + 1812q^{62} + 493q^{63} + 872q^{64} - 613q^{65} + 3073q^{66} + 295q^{67} + 2748q^{68} + 1389q^{69} - 1044q^{70} + 636q^{71} + 981q^{72} - 338q^{73} - 2238q^{74} - 1064q^{75} + 1006q^{76} - 2909q^{77} + 157q^{78} + 133q^{79} - 4817q^{80} + 1325q^{81} + 6q^{82} - 1356q^{83} - 7081q^{84} + 483q^{85} + 6686q^{86} + 2774q^{87} - 738q^{88} - 2200q^{89} + 2665q^{90} + 1552q^{91} - 396q^{92} + 4365q^{93} - 1191q^{94} + 3083q^{95} - 1468q^{96} - 266q^{97} + 3601q^{98} - 5395q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
63.4.g.a \(44\) \(3.717\) None \(1\) \(-1\) \(38\) \(-7\)