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Properties

Label 495.6.x
Level $495$
Weight $6$
Character orbit 495.x
Rep. character $\chi_{495}(116,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $320$
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.x (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 1472 320 1152
Cusp forms 1408 320 1088
Eisenstein series 64 0 64

Trace form

\( 320 q - 1280 q^{4} + O(q^{10}) \) \( 320 q - 1280 q^{4} - 23824 q^{16} + 35896 q^{22} + 50000 q^{25} - 37240 q^{28} - 30536 q^{31} + 16752 q^{34} + 16328 q^{37} - 104800 q^{46} + 109424 q^{49} + 107400 q^{55} + 375216 q^{58} - 197720 q^{61} - 705816 q^{64} + 48928 q^{67} - 19800 q^{70} + 367280 q^{73} - 314680 q^{79} - 680920 q^{82} - 180240 q^{88} + 1120624 q^{91} - 802640 q^{94} - 299960 q^{97} + O(q^{100}) \)

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.

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

\( S_{6}^{\mathrm{old}}(495, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)