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Properties

Label 546.8.u
Level $546$
Weight $8$
Character orbit 546.u
Rep. character $\chi_{546}(185,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $524$
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.u (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 524 1060
Cusp forms 1552 524 1028
Eisenstein series 32 0 32

Trace form

\( 524 q + 16768 q^{4} - 1950 q^{7} + 2296 q^{9} + O(q^{10}) \) \( 524 q + 16768 q^{4} - 1950 q^{7} + 2296 q^{9} + 1766 q^{13} + 3612 q^{15} - 1073152 q^{16} + 23040 q^{18} - 82328 q^{21} - 4156250 q^{25} - 88320 q^{28} + 31904 q^{30} + 36132 q^{31} + 73472 q^{36} + 532498 q^{37} - 994956 q^{39} + 767936 q^{42} - 1478266 q^{43} - 204064 q^{46} - 2995158 q^{49} - 679358 q^{51} + 1654912 q^{52} + 2133072 q^{54} + 3147000 q^{55} - 893704 q^{57} + 2735488 q^{58} - 231168 q^{60} - 3862624 q^{63} - 137363456 q^{64} - 1207104 q^{66} - 5367328 q^{67} - 10433334 q^{69} - 2182656 q^{70} + 2949120 q^{72} - 11926962 q^{73} + 17453508 q^{75} - 3063168 q^{76} - 11454816 q^{78} + 15367820 q^{79} + 2240360 q^{81} + 5268992 q^{84} - 13526824 q^{85} - 12789528 q^{87} + 54805680 q^{91} + 2337688 q^{93} - 57285042 q^{97} + 34997760 q^{99} + O(q^{100}) \)

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

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