↑

Properties

Label 441.6.g
Level $441$
Weight $6$
Character orbit 441.g
Rep. character $\chi_{441}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $392$
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.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 576 408 168
Cusp forms 544 392 152
Eisenstein series 32 16 16

Trace form

\( 392 q - q^{2} + q^{3} - 3073 q^{4} + 202 q^{5} + 116 q^{6} + 48 q^{8} - 409 q^{9} + O(q^{10}) \) \( 392 q - q^{2} + q^{3} - 3073 q^{4} + 202 q^{5} + 116 q^{6} + 48 q^{8} - 409 q^{9} + 66 q^{10} + 762 q^{11} - 1639 q^{12} - 179 q^{13} + 2854 q^{15} - 47137 q^{16} - 2043 q^{17} + 91 q^{18} + 64 q^{19} - 2782 q^{20} + 60 q^{22} + 10480 q^{23} + 1722 q^{24} + 225002 q^{25} - 4798 q^{26} + 5551 q^{27} + 3126 q^{29} + 14946 q^{30} - 1085 q^{31} + 2141 q^{32} + 9490 q^{33} - 30 q^{34} - 2992 q^{36} + 2581 q^{37} + 44510 q^{38} + 1784 q^{39} + 2028 q^{40} - 46630 q^{41} - 9248 q^{43} - 37565 q^{44} + 24598 q^{45} - 9606 q^{46} - 34755 q^{47} + 111629 q^{48} + 146415 q^{50} + 45154 q^{51} + 18946 q^{52} - 26012 q^{53} - 114778 q^{54} - 22314 q^{55} - 99717 q^{57} - 10158 q^{58} - 93390 q^{59} - 81442 q^{60} + 48142 q^{61} + 301716 q^{62} + 1378352 q^{64} - 3684 q^{65} - 122185 q^{66} + 622 q^{67} + 277044 q^{68} - 253152 q^{69} + 942 q^{71} + 160395 q^{72} + 42016 q^{73} + 64802 q^{74} + 53477 q^{75} + 3010 q^{76} + 383085 q^{78} + 48574 q^{79} - 190471 q^{80} + 365903 q^{81} - 30 q^{82} - 177090 q^{83} + 14571 q^{85} - 24554 q^{86} + 146863 q^{87} + 61698 q^{88} - 176927 q^{89} + 238307 q^{90} + 191714 q^{92} + 317620 q^{93} - 96369 q^{94} - 239057 q^{95} + 136972 q^{96} + 34681 q^{97} + 403910 q^{99} + O(q^{100}) \)

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

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