Properties

Label 441.4.ba
Level $441$
Weight $4$
Character orbit 441.ba
Rep. character $\chi_{441}(22,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1992$
Sturm bound $224$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.ba (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

\( 1992q - 5q^{2} - 10q^{3} + 651q^{4} + 15q^{5} + 14q^{6} - 52q^{8} + 60q^{9} + O(q^{10}) \) \( 1992q - 5q^{2} - 10q^{3} + 651q^{4} + 15q^{5} + 14q^{6} - 52q^{8} + 60q^{9} - 52q^{10} - 5q^{11} - 355q^{12} - 29q^{13} + 172q^{14} + 20q^{15} + 2571q^{16} - 196q^{17} + 2q^{18} + 72q^{19} - 5q^{20} + 21q^{21} - 37q^{22} + 205q^{23} + 550q^{24} + 3945q^{25} - 836q^{26} + 104q^{27} - 360q^{28} - 215q^{29} - 798q^{30} + 108q^{31} - 889q^{32} + 200q^{33} + 11q^{34} + 526q^{35} - 3178q^{36} - 860q^{37} - 169q^{38} + 76q^{39} + 341q^{40} + 583q^{41} + 3496q^{42} - 173q^{43} + 1232q^{44} - 456q^{45} - 2572q^{46} + 1265q^{47} + 490q^{48} - 324q^{49} - 18q^{50} + 1050q^{51} + 715q^{52} - 4276q^{53} - 4362q^{54} + 2540q^{55} + 2887q^{56} - 3192q^{57} - 1297q^{58} + 911q^{59} - 4676q^{60} - 2069q^{61} - 2220q^{62} - 141q^{63} - 19764q^{64} - 1289q^{65} + 984q^{66} + 576q^{67} - 8906q^{68} + 7924q^{69} + 311q^{70} + 5720q^{71} + 3728q^{72} - 692q^{73} + 459q^{74} - 4806q^{75} - 1317q^{76} - 788q^{77} + 7350q^{78} - 684q^{79} + 35536q^{80} - 1004q^{81} - 52q^{82} + 3067q^{83} - 14684q^{84} + 245q^{85} - 4713q^{86} - 896q^{87} + 779q^{88} + 5476q^{89} + 7308q^{90} + 1030q^{91} - 8239q^{92} + 9001q^{93} + 1187q^{94} + 994q^{95} - 1299q^{96} - 540q^{97} - 22044q^{98} + 14954q^{99} + O(q^{100}) \)

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

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