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Properties

Label 546.8.bu
Level $546$
Weight $8$
Character orbit 546.bu
Rep. character $\chi_{546}(71,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $784$
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.bu (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 3168 784 2384
Cusp forms 3104 784 2320
Eisenstein series 64 0 64

Trace form

\( 784 q + O(q^{10}) \) \( 784 q + 31872 q^{10} - 16176 q^{13} - 14112 q^{15} + 1605632 q^{16} - 50624 q^{18} + 56656 q^{19} - 112504 q^{21} + 741264 q^{27} + 807744 q^{30} + 146288 q^{31} - 1184712 q^{33} - 300672 q^{34} + 440832 q^{36} + 331088 q^{37} + 3671536 q^{39} - 5323504 q^{45} - 1536832 q^{46} - 2975808 q^{54} + 923536 q^{55} + 19449160 q^{57} + 1029824 q^{58} + 462336 q^{60} - 710096 q^{61} + 2464112 q^{63} - 12042752 q^{66} + 4325760 q^{67} - 25109208 q^{69} + 6479872 q^{72} + 10446448 q^{73} + 28304640 q^{75} + 3625984 q^{76} - 43540544 q^{78} - 7041376 q^{79} + 28193784 q^{81} + 7200256 q^{84} + 16944736 q^{85} + 15437744 q^{91} + 53122728 q^{93} - 14391424 q^{94} - 7632896 q^{97} + 118966480 q^{99} + O(q^{100}) \)

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

\( S_{8}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)