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Properties

Label 819.6.bm
Level $819$
Weight $6$
Character orbit 819.bm
Rep. character $\chi_{819}(478,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $462$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 819.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(819, [\chi])\).

Total New Old
Modular forms 1136 470 666
Cusp forms 1104 462 642
Eisenstein series 32 8 24

Trace form

\( 462 q - 7298 q^{4} - 127 q^{7} + O(q^{10}) \) \( 462 q - 7298 q^{4} - 127 q^{7} + 465 q^{10} + 33 q^{11} + 580 q^{13} + 860 q^{14} + 112966 q^{16} + 5710 q^{17} + 108 q^{19} - 2622 q^{20} + 3768 q^{22} - 3426 q^{23} + 138061 q^{25} - 22074 q^{26} - 7385 q^{28} + 556 q^{29} + 2181 q^{31} + 17523 q^{35} - 4882 q^{38} - 29842 q^{40} + 6927 q^{41} - 5248 q^{43} + 11868 q^{44} + 69660 q^{47} + 20559 q^{49} + 138378 q^{50} - 85351 q^{52} - 32683 q^{53} - 64764 q^{55} + 45309 q^{56} + 76377 q^{58} - 73558 q^{61} - 104408 q^{62} - 1704904 q^{64} + 155850 q^{65} + 175716 q^{67} - 240034 q^{68} - 116658 q^{70} + 105969 q^{71} + 109491 q^{73} - 195138 q^{74} + 30906 q^{76} + 173230 q^{77} - 98072 q^{79} + 348954 q^{80} - 42526 q^{82} + 1617 q^{85} + 415242 q^{86} - 287123 q^{88} + 329313 q^{91} + 190866 q^{92} - 374516 q^{94} + 28258 q^{95} + 598134 q^{97} - 416622 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(819, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(819, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(819, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)