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Properties

Label 495.6.bs
Level $495$
Weight $6$
Character orbit 495.bs
Rep. character $\chi_{495}(7,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $5696$
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.bs (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 495 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 5824 5824 0
Cusp forms 5696 5696 0
Eisenstein series 128 128 0

Trace form

\( 5696 q - 10 q^{2} - 14 q^{3} - 6 q^{5} - 40 q^{6} - 10 q^{7} - 40 q^{8} + O(q^{10}) \) \( 5696 q - 10 q^{2} - 14 q^{3} - 6 q^{5} - 40 q^{6} - 10 q^{7} - 40 q^{8} + 364 q^{11} + 556 q^{12} - 10 q^{13} + 1900 q^{15} - 176140 q^{16} - 40 q^{17} - 20 q^{18} + 4474 q^{20} + 120 q^{22} - 24032 q^{23} - 3312 q^{25} - 3568 q^{26} - 5756 q^{27} - 40 q^{28} - 20 q^{30} - 12 q^{31} - 37274 q^{33} - 40 q^{35} + 56568 q^{36} - 20052 q^{37} - 48982 q^{38} - 10250 q^{40} - 20 q^{41} + 113536 q^{42} + 8596 q^{45} - 80 q^{46} + 21122 q^{47} - 79704 q^{48} - 10 q^{50} + 247560 q^{51} - 10 q^{52} - 345504 q^{53} - 12532 q^{55} - 79128 q^{56} + 287900 q^{57} + 29834 q^{58} - 161752 q^{60} - 20 q^{61} - 675340 q^{62} - 20 q^{63} + 89732 q^{66} + 22040 q^{67} - 650 q^{68} + 24994 q^{70} + 185032 q^{71} + 449830 q^{72} - 40 q^{73} - 150772 q^{75} - 292220 q^{77} + 169464 q^{78} - 1571792 q^{80} + 848676 q^{81} + 232 q^{82} - 10 q^{83} - 10 q^{85} - 649452 q^{86} - 779560 q^{88} - 668680 q^{90} + 193992 q^{91} - 857314 q^{92} + 594542 q^{93} - 10 q^{95} + 1060260 q^{96} - 52992 q^{97} + O(q^{100}) \)

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.