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Properties

Label 495.6.bc
Level $495$
Weight $6$
Character orbit 495.bc
Rep. character $\chi_{495}(23,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1200$
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.bc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 1200 256
Cusp forms 1424 1200 224
Eisenstein series 32 0 32

Trace form

\( 1200 q + 2 q^{3} + 320 q^{6} + O(q^{10}) \) \( 1200 q + 2 q^{3} + 320 q^{6} - 128 q^{12} - 4084 q^{15} + 153600 q^{16} - 10632 q^{18} + 11136 q^{20} + 880 q^{21} + 31632 q^{23} - 3306 q^{25} - 14428 q^{27} - 18808 q^{30} - 28920 q^{32} + 15004 q^{33} - 72960 q^{36} + 20028 q^{37} - 81480 q^{41} + 107824 q^{42} + 79612 q^{45} + 31920 q^{46} - 2124 q^{47} + 136024 q^{48} - 79840 q^{51} + 27588 q^{55} - 23040 q^{56} - 108604 q^{57} + 276080 q^{60} + 93480 q^{61} - 183928 q^{63} + 215856 q^{65} + 5514 q^{67} + 205056 q^{68} + 303768 q^{72} - 505972 q^{75} + 100680 q^{76} - 719492 q^{78} + 277660 q^{81} - 552576 q^{82} - 163248 q^{85} + 1113480 q^{86} + 212744 q^{87} + 53056 q^{90} + 1518336 q^{92} + 947726 q^{93} + 7320 q^{95} - 72560 q^{96} + 192726 q^{97} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(495, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)