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Properties

Label 546.8.bq
Level $546$
Weight $8$
Character orbit 546.bq
Rep. character $\chi_{546}(419,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $520$
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.bq (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
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 520 1064
Cusp forms 1552 520 1032
Eisenstein series 32 0 32

Trace form

\( 520 q + 16640 q^{4} - 944 q^{7} - 1148 q^{9} + O(q^{10}) \) \( 520 q + 16640 q^{4} - 944 q^{7} - 1148 q^{9} + 3612 q^{15} - 1064960 q^{16} - 59712 q^{18} + 164656 q^{21} + 7875000 q^{25} + 60416 q^{28} + 435776 q^{30} + 73472 q^{36} + 128448 q^{37} - 2897184 q^{39} + 767936 q^{42} + 279844 q^{43} - 204064 q^{46} - 3122920 q^{49} - 3035120 q^{51} - 893704 q^{57} - 1367744 q^{58} + 462336 q^{60} - 28216 q^{63} - 136314880 q^{64} + 4940004 q^{67} + 4365312 q^{70} - 1910784 q^{72} + 13812768 q^{78} - 73569360 q^{79} + 11833160 q^{81} + 5268992 q^{84} + 11240648 q^{85} + 2648288 q^{91} - 25660088 q^{93} + 34997760 q^{99} + O(q^{100}) \)

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

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