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Properties

Label 495.6.bf
Level $495$
Weight $6$
Character orbit 495.bf
Rep. character $\chi_{495}(43,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1424$
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.bf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 495 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 1456 1456 0
Cusp forms 1424 1424 0
Eisenstein series 32 32 0

Trace form

\( 1424 q - 6 q^{3} - 4 q^{5} + O(q^{10}) \) \( 1424 q - 6 q^{3} - 4 q^{5} - 384 q^{11} - 1236 q^{12} - 1920 q^{15} + 176120 q^{16} - 4484 q^{20} - 130 q^{22} - 6008 q^{23} + 3302 q^{25} + 3488 q^{26} + 5736 q^{27} - 8 q^{31} - 12296 q^{33} + 70992 q^{36} + 20012 q^{37} - 32868 q^{38} - 113876 q^{42} - 8636 q^{45} - 21132 q^{47} + 69444 q^{48} + 345464 q^{53} + 12492 q^{55} + 79088 q^{56} + 20316 q^{58} + 317252 q^{60} - 89772 q^{66} + 5510 q^{67} - 25004 q^{70} - 185112 q^{71} - 281328 q^{75} - 235710 q^{77} - 169504 q^{78} + 1571752 q^{80} - 54516 q^{81} - 272 q^{82} - 432968 q^{86} - 118170 q^{88} + 129328 q^{91} + 836824 q^{92} - 428902 q^{93} + 52982 q^{97} + O(q^{100}) \)

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.