↑

Properties

Label 441.6.f
Level $441$
Weight $6$
Character orbit 441.f
Rep. character $\chi_{441}(148,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $400$
Sturm bound $336$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(441, [\chi])\).

Total New Old
Modular forms 576 420 156
Cusp forms 544 400 144
Eisenstein series 32 20 12

Trace form

\( 400 q + 5 q^{2} - 8 q^{3} - 3119 q^{4} - 20 q^{5} - 49 q^{6} - 894 q^{8} + 410 q^{9} + O(q^{10}) \) \( 400 q + 5 q^{2} - 8 q^{3} - 3119 q^{4} - 20 q^{5} - 49 q^{6} - 894 q^{8} + 410 q^{9} - 60 q^{10} + 66 q^{11} + 1088 q^{12} + 182 q^{13} - 1556 q^{15} - 47327 q^{16} + 1344 q^{17} - 2678 q^{18} + 836 q^{19} - 2146 q^{20} + 879 q^{22} + 3508 q^{23} - 7767 q^{24} - 114152 q^{25} + 4592 q^{26} - 6140 q^{27} - 2766 q^{29} - 10674 q^{30} + 3302 q^{31} + 19649 q^{32} - 26336 q^{33} + 10191 q^{34} - 4129 q^{36} - 4852 q^{37} - 18427 q^{38} - 30298 q^{39} - 564 q^{40} + 13826 q^{41} + 12392 q^{43} + 69766 q^{44} + 19360 q^{45} + 8304 q^{46} - 63090 q^{47} - 46279 q^{48} + 60045 q^{50} + 6328 q^{51} - 13372 q^{52} - 153128 q^{53} + 60209 q^{54} + 8532 q^{55} - 109968 q^{57} - 1830 q^{58} - 61776 q^{59} + 181634 q^{60} - 48142 q^{61} + 7380 q^{62} + 1351090 q^{64} + 17994 q^{65} + 261320 q^{66} - 8392 q^{67} - 172869 q^{68} + 107694 q^{69} - 146364 q^{71} + 120477 q^{72} + 38432 q^{73} + 203054 q^{74} - 35794 q^{75} - 43681 q^{76} + 494496 q^{78} + 59516 q^{79} + 399944 q^{80} - 253150 q^{81} - 233718 q^{82} - 24126 q^{83} + 52782 q^{85} - 70817 q^{86} - 404060 q^{87} + 165837 q^{88} - 18812 q^{89} - 397996 q^{90} + 223034 q^{92} + 416182 q^{93} + 73098 q^{94} + 9742 q^{95} + 297208 q^{96} - 35380 q^{97} + 526172 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)