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Properties

Label 546.8.bk
Level $546$
Weight $8$
Character orbit 546.bk
Rep. character $\chi_{546}(25,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $264$
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.bk (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 264 1320
Cusp forms 1552 264 1288
Eisenstein series 32 0 32

Trace form

\( 264 q + 8448 q^{4} - 96228 q^{9} + O(q^{10}) \) \( 264 q + 8448 q^{4} - 96228 q^{9} - 8000 q^{10} + 25480 q^{13} - 14368 q^{14} - 540672 q^{16} + 20668 q^{17} - 16064 q^{22} + 72856 q^{23} + 2117668 q^{25} - 113312 q^{26} - 693944 q^{29} - 2176552 q^{35} - 12317184 q^{36} - 353888 q^{38} + 258444 q^{39} + 512000 q^{40} - 3213760 q^{43} - 1272844 q^{49} + 1065744 q^{51} + 815360 q^{52} - 3225604 q^{53} + 3583168 q^{55} - 2533376 q^{56} + 5245236 q^{61} - 8801792 q^{62} - 69206016 q^{64} - 11445508 q^{65} + 4599936 q^{66} - 1322752 q^{68} + 6460560 q^{69} + 1493568 q^{74} + 5660496 q^{75} + 46940176 q^{77} - 3540672 q^{78} + 8013416 q^{79} - 70150212 q^{81} - 18636800 q^{82} + 6822792 q^{87} - 514048 q^{88} + 11664000 q^{90} - 4025116 q^{91} + 9325568 q^{92} + 35622944 q^{94} - 37198224 q^{95} + O(q^{100}) \)

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

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