Properties

Label 441.4.y
Level $441$
Weight $4$
Character orbit 441.y
Rep. character $\chi_{441}(25,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1992$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.y (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(441, [\chi])\).

Total New Old
Modular forms 2040 2040 0
Cusp forms 1992 1992 0
Eisenstein series 48 48 0

Trace form

\( 1992q - 5q^{2} - 13q^{3} - 1317q^{4} + 12q^{5} - 22q^{6} - 4q^{8} + 57q^{9} + O(q^{10}) \) \( 1992q - 5q^{2} - 13q^{3} - 1317q^{4} + 12q^{5} - 22q^{6} - 4q^{8} + 57q^{9} - 10q^{10} - 8q^{11} + 818q^{12} + 7q^{13} + 220q^{14} - 25q^{15} - 5109q^{16} + 134q^{17} + 173q^{18} - 72q^{19} + 355q^{20} + 45q^{21} + 11q^{22} - 554q^{23} - 44q^{24} + 3942q^{25} + 238q^{26} - 202q^{27} + 144q^{28} + 541q^{29} - 246q^{30} + 108q^{31} - 793q^{32} - 91q^{33} - 13q^{34} - 317q^{35} + 1658q^{36} - 1118q^{37} + 698q^{38} - 266q^{39} + 11q^{40} + 685q^{41} - 2870q^{42} + 79q^{43} + 479q^{44} + 2427q^{45} - 3286q^{46} - 1555q^{47} + 985q^{48} - 324q^{49} - 9q^{50} - 795q^{51} - 2360q^{52} + 1850q^{53} - 591q^{54} - 1300q^{55} + 5245q^{56} + 1581q^{57} + 3284q^{58} - 3337q^{59} - 3239q^{60} - 2069q^{61} - 1896q^{62} - 2886q^{63} - 19332q^{64} - 1289q^{65} - 10710q^{66} + 576q^{67} - 10043q^{68} - 6863q^{69} - 1258q^{70} - 2890q^{71} + 2030q^{72} + 310q^{73} - 216q^{74} + 4179q^{75} - 117q^{76} - 2276q^{77} - 13893q^{78} - 684q^{79} - 10877q^{80} - 2351q^{81} - 34q^{82} + 1741q^{83} - 5747q^{84} - 130q^{85} + 2346q^{86} + 6469q^{87} - 376q^{88} - 2588q^{89} - 23826q^{90} - 1580q^{91} + 18077q^{92} + 13381q^{93} - 2389q^{94} + 2869q^{95} - 11244q^{96} + 252q^{97} + 9027q^{98} - 7513q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.