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Properties

Label 546.8.bz
Level $546$
Weight $8$
Character orbit 546.bz
Rep. character $\chi_{546}(31,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $528$
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.bz (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(546, [\chi])\).

Total New Old
Modular forms 3168 528 2640
Cusp forms 3104 528 2576
Eisenstein series 64 0 64

Trace form

\( 528 q + 560 q^{7} + 192456 q^{9} + O(q^{10}) \) \( 528 q + 560 q^{7} + 192456 q^{9} - 6056 q^{11} + 7232 q^{14} + 1081344 q^{16} - 281520 q^{19} + 135864 q^{21} - 32128 q^{22} + 143360 q^{28} + 324816 q^{29} - 572880 q^{31} + 926000 q^{35} + 481840 q^{37} - 516888 q^{39} - 387584 q^{44} - 11136 q^{46} - 4411904 q^{50} + 698880 q^{52} + 2800456 q^{53} + 1552176 q^{57} + 5106752 q^{58} - 5475144 q^{61} + 2041200 q^{63} - 9149072 q^{65} + 5273352 q^{67} - 7936512 q^{68} + 17830528 q^{70} + 28032208 q^{71} + 1579008 q^{73} - 20100992 q^{74} + 5104512 q^{78} - 11203712 q^{79} - 140300424 q^{81} - 4326912 q^{84} + 59287792 q^{85} - 11524672 q^{86} + 40936752 q^{87} + 63157152 q^{89} + 61780976 q^{91} + 18651136 q^{92} - 18983160 q^{93} - 19752000 q^{94} - 36556800 q^{98} - 8829648 q^{99} + O(q^{100}) \)

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

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