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Properties

Label 495.6.p
Level $495$
Weight $6$
Character orbit 495.p
Rep. character $\chi_{495}(131,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $480$
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.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 728 480 248
Cusp forms 712 480 232
Eisenstein series 16 0 16

Trace form

\( 480 q - 44 q^{3} - 3840 q^{4} - 308 q^{9} + O(q^{10}) \) \( 480 q - 44 q^{3} - 3840 q^{4} - 308 q^{9} + 804 q^{11} + 4224 q^{12} - 1100 q^{15} - 61440 q^{16} + 1896 q^{22} + 396 q^{23} + 150000 q^{25} + 2596 q^{27} + 47960 q^{33} + 15312 q^{34} - 54072 q^{36} + 39228 q^{38} + 100712 q^{42} + 27220 q^{48} + 576240 q^{49} + 143220 q^{56} + 137280 q^{59} - 62700 q^{60} + 1966080 q^{64} - 216468 q^{66} + 42108 q^{67} - 267212 q^{69} + 27500 q^{75} + 160974 q^{77} - 223780 q^{78} + 278348 q^{81} - 222816 q^{82} - 136848 q^{86} + 91008 q^{88} + 64680 q^{91} - 206004 q^{92} - 295396 q^{93} + 348876 q^{97} - 531452 q^{99} + O(q^{100}) \)

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

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