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Properties

Label 546.8.bg
Level $546$
Weight $8$
Character orbit 546.bg
Rep. character $\chi_{546}(311,\cdot)$
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.bg (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

\( 520 q - 16640 q^{4} - 2296 q^{9} + O(q^{10}) \) \( 520 q - 16640 q^{4} - 2296 q^{9} - 1064960 q^{16} + 3937500 q^{25} - 118672 q^{30} + 293888 q^{36} + 384696 q^{39} + 315136 q^{42} - 828256 q^{43} + 2934256 q^{49} + 450066 q^{51} - 1767936 q^{52} + 11026776 q^{61} + 136314880 q^{64} - 2414208 q^{66} - 54749412 q^{75} + 3776320 q^{78} - 47518024 q^{79} - 17269960 q^{81} - 29444736 q^{82} - 25579056 q^{87} - 9240116 q^{91} - 27547776 q^{94} + O(q^{100}) \)

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

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