Properties

Label 63.4.h
Level $63$
Weight $4$
Character orbit 63.h
Rep. character $\chi_{63}(25,\cdot)$
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.h (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

\( 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} + O(q^{10}) \) \( 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} - 18q^{10} + 5q^{11} - 62q^{12} - 14q^{13} - 52q^{14} + 119q^{15} + 494q^{16} - 162q^{17} - 188q^{18} + 58q^{19} - 362q^{20} - 59q^{21} - 18q^{22} - 93q^{23} + 30q^{24} - 349q^{25} - 266q^{26} + 272q^{27} - 172q^{28} + 248q^{29} + 85q^{30} - 122q^{31} + 326q^{32} + 77q^{33} + 6q^{34} + 289q^{35} - 806q^{36} - 86q^{37} - 761q^{38} - 256q^{39} - 18q^{40} - 692q^{41} - 364q^{42} - 86q^{43} - 443q^{44} + 527q^{45} - 270q^{46} + 2010q^{47} - 1013q^{48} + 317q^{49} + 239q^{50} + 1209q^{51} - 335q^{52} + 258q^{53} + 577q^{54} - 870q^{55} - 1752q^{56} + 566q^{57} + 237q^{58} + 3330q^{59} + 1669q^{60} - 878q^{61} + 1812q^{62} + 2872q^{63} + 872q^{64} + 1226q^{65} + 1330q^{66} - 590q^{67} - 1374q^{68} + 1389q^{69} + 1251q^{70} + 636q^{71} - 5970q^{72} - 338q^{73} + 1119q^{74} + 2737q^{75} + 1006q^{76} + 2269q^{77} + 157q^{78} - 266q^{79} - 4817q^{80} - 505q^{81} + 6q^{82} - 1356q^{83} - 6013q^{84} + 483q^{85} - 3343q^{86} - 5755q^{87} + 369q^{88} - 2200q^{89} + 2665q^{90} + 1552q^{91} - 396q^{92} - 129q^{93} + 2382q^{94} - 6166q^{95} - 5941q^{96} - 266q^{97} + 3601q^{98} - 5395q^{99} + O(q^{100}) \)

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.h.a \(44\) \(3.717\) None \(-2\) \(-1\) \(-19\) \(-7\)