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Properties

Label 495.6.i
Level $495$
Weight $6$
Character orbit 495.i
Rep. character $\chi_{495}(166,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $400$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 495.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(495, [\chi])\).

Total New Old
Modular forms 728 400 328
Cusp forms 712 400 312
Eisenstein series 16 0 16

Trace form

\( 400 q - 3200 q^{4} + 100 q^{5} + 388 q^{6} + 116 q^{7} - 1704 q^{8} - 380 q^{9} + O(q^{10}) \) \( 400 q - 3200 q^{4} + 100 q^{5} + 388 q^{6} + 116 q^{7} - 1704 q^{8} - 380 q^{9} + 5324 q^{12} - 724 q^{13} + 2100 q^{14} - 51200 q^{16} - 7072 q^{18} + 248 q^{19} + 4800 q^{20} + 4480 q^{21} + 12696 q^{23} + 3608 q^{24} - 125000 q^{25} - 44112 q^{26} - 7464 q^{27} - 14848 q^{28} + 11940 q^{29} + 7600 q^{30} - 4336 q^{31} + 19624 q^{32} + 12660 q^{34} + 23348 q^{36} - 20632 q^{37} + 24676 q^{38} - 8008 q^{39} - 9300 q^{40} - 24060 q^{41} - 61484 q^{42} - 36976 q^{43} + 29600 q^{45} + 91800 q^{46} + 126064 q^{47} - 184260 q^{48} - 459384 q^{49} + 95464 q^{51} - 138100 q^{52} - 88144 q^{53} + 336204 q^{54} - 87960 q^{56} - 24080 q^{57} + 12996 q^{58} - 38216 q^{59} + 145832 q^{61} + 228168 q^{62} + 512912 q^{63} + 1536688 q^{64} - 99220 q^{66} + 2492 q^{67} - 186980 q^{68} - 122244 q^{69} + 73200 q^{70} + 361664 q^{71} - 12912 q^{72} + 168056 q^{73} - 61160 q^{74} - 58276 q^{76} + 94864 q^{77} - 127000 q^{78} + 85076 q^{79} - 358400 q^{80} - 177180 q^{81} - 604872 q^{82} + 253576 q^{83} + 351344 q^{84} + 54196 q^{86} - 399272 q^{87} - 492088 q^{89} + 71100 q^{90} + 440488 q^{91} - 354580 q^{92} + 556752 q^{93} + 465636 q^{94} + 35800 q^{95} + 951112 q^{96} + 138716 q^{97} + 957304 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(495, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(495, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)