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Properties

Label 546.8.bd
Level $546$
Weight $8$
Character orbit 546.bd
Rep. character $\chi_{546}(121,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $260$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 546.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(546, [\chi])\).

Total New Old
Modular forms 1584 260 1324
Cusp forms 1552 260 1292
Eisenstein series 32 0 32

Trace form

\( 260 q - 108 q^{3} + 8320 q^{4} + 1514 q^{7} + 189540 q^{9} + O(q^{10}) \) \( 260 q - 108 q^{3} + 8320 q^{4} + 1514 q^{7} + 189540 q^{9} + 16000 q^{10} - 3456 q^{12} - 9046 q^{13} + 12608 q^{14} - 532480 q^{16} + 20668 q^{17} - 94878 q^{21} + 8032 q^{22} + 72856 q^{23} + 1898918 q^{25} - 113312 q^{26} - 78732 q^{27} + 32512 q^{28} + 346972 q^{29} + 286440 q^{31} - 891388 q^{35} + 6065280 q^{36} - 1181010 q^{37} - 353888 q^{38} - 694494 q^{39} + 512000 q^{40} - 2546244 q^{41} - 1045782 q^{43} + 581376 q^{44} - 612192 q^{46} + 7130664 q^{47} + 221184 q^{48} + 1244770 q^{49} - 3308928 q^{50} - 678348 q^{51} + 928384 q^{52} - 487540 q^{53} - 677708 q^{55} - 112640 q^{56} - 11002876 q^{61} - 1033952 q^{62} + 1103706 q^{63} - 68157440 q^{64} - 4335604 q^{65} + 4599936 q^{66} - 1322752 q^{68} - 3230280 q^{69} + 4536960 q^{70} + 11808684 q^{71} + 2690394 q^{73} - 746784 q^{74} - 8736498 q^{75} + 3042432 q^{76} + 18033724 q^{77} + 5598720 q^{78} + 4935136 q^{79} + 138174660 q^{81} + 7828864 q^{82} - 5633280 q^{84} + 47090424 q^{85} + 18055584 q^{86} - 3411396 q^{87} + 1028096 q^{88} + 8647608 q^{89} + 11664000 q^{90} + 9675792 q^{91} + 9325568 q^{92} + 12145788 q^{93} - 31871872 q^{94} + 28816032 q^{95} - 60516054 q^{97} - 24044352 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(546, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(546, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)