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Properties

Label 546.8.bm
Level $546$
Weight $8$
Character orbit 546.bm
Rep. character $\chi_{546}(205,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $260$
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.bm (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 260 1324
Cusp forms 1552 260 1292
Eisenstein series 32 0 32

Trace form

\( 260 q + 54 q^{3} - 16640 q^{4} + 1006 q^{7} - 94770 q^{9} + O(q^{10}) \) \( 260 q + 54 q^{3} - 16640 q^{4} + 1006 q^{7} - 94770 q^{9} - 8000 q^{10} + 9084 q^{11} - 3456 q^{12} - 9046 q^{13} + 12608 q^{14} + 1064960 q^{16} - 41336 q^{17} - 47538 q^{19} + 94878 q^{21} + 8032 q^{22} - 145712 q^{23} + 1898918 q^{25} - 113312 q^{26} - 78732 q^{27} - 64384 q^{28} + 346972 q^{29} - 286440 q^{31} - 196888 q^{35} + 6065280 q^{36} - 353888 q^{38} + 41472 q^{39} + 512000 q^{40} - 2546244 q^{41} - 1045782 q^{43} - 581376 q^{44} - 7130664 q^{47} + 221184 q^{48} + 362686 q^{49} - 3308928 q^{50} - 678348 q^{51} + 578944 q^{52} - 487540 q^{53} - 677708 q^{55} - 806912 q^{56} + 9711744 q^{58} + 5501438 q^{61} - 1033952 q^{62} + 370332 q^{63} - 68157440 q^{64} - 9578152 q^{65} + 4599936 q^{66} - 6033300 q^{67} + 2645504 q^{68} - 3230280 q^{69} - 4536960 q^{70} + 11808684 q^{71} - 2690394 q^{73} + 1493568 q^{74} + 17472996 q^{75} + 3042432 q^{76} + 18033724 q^{77} + 5598720 q^{78} + 4935136 q^{79} - 69087330 q^{81} - 3914432 q^{82} - 6072192 q^{84} + 47090424 q^{85} - 18055584 q^{86} + 6822792 q^{87} - 514048 q^{88} + 11664000 q^{90} + 27041380 q^{91} + 9325568 q^{92} + 15935936 q^{94} - 57632064 q^{95} - 60516054 q^{97} - 17297856 q^{98} + O(q^{100}) \)

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

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