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Properties

Label 546.8.z
Level $546$
Weight $8$
Character orbit 546.z
Rep. character $\chi_{546}(131,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $448$
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.z (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 448 1136
Cusp forms 1552 448 1104
Eisenstein series 32 0 32

Trace form

\( 448 q + 14336 q^{4} + 1348 q^{7} - 1508 q^{9} + O(q^{10}) \) \( 448 q + 14336 q^{4} + 1348 q^{7} - 1508 q^{9} - 1248 q^{10} + 50376 q^{15} - 917504 q^{16} + 182272 q^{21} + 117312 q^{22} - 178176 q^{24} - 3642012 q^{25} - 86272 q^{28} + 98576 q^{30} + 38292 q^{31} - 193024 q^{36} - 464640 q^{37} - 79872 q^{40} + 624032 q^{42} - 4392128 q^{43} - 9073512 q^{45} - 2225920 q^{46} - 7832716 q^{49} + 1330150 q^{51} + 2310128 q^{57} - 2228960 q^{58} + 1612032 q^{60} + 15461784 q^{61} - 5555032 q^{63} - 117440512 q^{64} + 1252992 q^{66} - 22324128 q^{70} + 8886432 q^{73} - 35361636 q^{75} + 8654052 q^{79} + 3784100 q^{81} - 2215936 q^{84} + 36059456 q^{85} + 5973396 q^{87} + 3753984 q^{88} + 8401328 q^{91} - 24496604 q^{93} - 11403264 q^{96} + 8580096 q^{99} + O(q^{100}) \)

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

\( S_{8}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)