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Properties

Label 546.8.bb
Level $546$
Weight $8$
Character orbit 546.bb
Rep. character $\chi_{546}(269,\cdot)$
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.bb (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

\( 524 q - 33536 q^{4} + 570 q^{7} - 1148 q^{9} + O(q^{10}) \) \( 524 q - 33536 q^{4} + 570 q^{7} - 1148 q^{9} - 1766 q^{13} + 3612 q^{15} + 2146304 q^{16} + 23040 q^{18} - 47862 q^{19} - 82328 q^{21} - 4156250 q^{25} - 36480 q^{28} - 15952 q^{30} + 36132 q^{31} - 2151504 q^{33} + 73472 q^{36} - 1064996 q^{37} + 602958 q^{39} - 1440976 q^{42} - 1478266 q^{43} + 408128 q^{46} - 462822 q^{49} - 679358 q^{51} + 113024 q^{52} - 3147000 q^{55} - 893704 q^{57} - 1367744 q^{58} - 231168 q^{60} - 19717074 q^{61} - 5624134 q^{63} - 137363456 q^{64} - 1207104 q^{66} + 2683664 q^{67} + 10433334 q^{69} - 2182656 q^{70} - 1474560 q^{72} - 11926962 q^{73} + 3063168 q^{76} - 11454816 q^{78} + 15367820 q^{79} - 1120180 q^{81} - 14722368 q^{82} + 5268992 q^{84} - 13526824 q^{85} + 2265976 q^{91} - 4675376 q^{93} + 23234880 q^{94} + 57285042 q^{97} + 34997760 q^{99} + O(q^{100}) \)

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

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