↑

Properties

Label 441.4.h
Level $441$
Weight $4$
Character orbit 441.h
Rep. character $\chi_{441}(214,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $232$
Sturm bound $224$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(224\)

Dimensions

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

Total New Old
Modular forms 352 248 104
Cusp forms 320 232 88
Eisenstein series 32 16 16

Trace form

\( 232 q + 2 q^{2} + q^{3} + 898 q^{4} + 19 q^{5} + 20 q^{6} + 5 q^{9} + O(q^{10}) \) \( 232 q + 2 q^{2} + q^{3} + 898 q^{4} + 19 q^{5} + 20 q^{6} + 5 q^{9} + 18 q^{10} - 9 q^{11} + 62 q^{12} + 14 q^{13} - 239 q^{15} + 3346 q^{16} + 162 q^{17} + 100 q^{18} - 58 q^{19} + 362 q^{20} + 12 q^{22} + 145 q^{23} - 30 q^{24} - 2501 q^{25} + 266 q^{26} - 272 q^{27} - 462 q^{29} + 231 q^{30} + 122 q^{31} - 58 q^{32} - 77 q^{33} - 6 q^{34} + 1160 q^{36} + 86 q^{37} + 761 q^{38} + 764 q^{39} + 18 q^{40} + 692 q^{41} + 80 q^{43} - 5 q^{44} - 527 q^{45} + 222 q^{46} - 2010 q^{47} + 1013 q^{48} - 489 q^{50} - 1475 q^{51} + 335 q^{52} - 434 q^{53} - 577 q^{54} + 870 q^{55} - 198 q^{57} - 237 q^{58} - 3330 q^{59} - 3001 q^{60} + 878 q^{61} - 1812 q^{62} + 11392 q^{64} - 1170 q^{65} - 1330 q^{66} + 590 q^{67} + 1374 q^{68} - 1389 q^{69} - 1668 q^{71} + 8232 q^{72} + 338 q^{73} - 2077 q^{74} - 2737 q^{75} - 1006 q^{76} + 2109 q^{78} + 1202 q^{79} + 4817 q^{80} + 701 q^{81} - 6 q^{82} + 1356 q^{83} - 849 q^{85} + 4333 q^{86} + 5755 q^{87} - 417 q^{88} + 2200 q^{89} - 2665 q^{90} + 1322 q^{92} + 469 q^{93} - 2382 q^{94} + 12706 q^{95} + 5941 q^{96} + 266 q^{97} + 1967 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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

Decomposition of \(S_{4}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(441, [\chi]) \cong \)