Properties

Label 546.8.k
Level $546$
Weight $8$
Character orbit 546.k
Rep. character $\chi_{546}(373,\cdot)$
Character field $\Q(\zeta_{3})$
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.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
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

\( 260 q + 108 q^{3} - 8320 q^{4} - 1286 q^{7} + 189540 q^{9} + O(q^{10}) \) \( 260 q + 108 q^{3} - 8320 q^{4} - 1286 q^{7} + 189540 q^{9} + 16000 q^{10} - 6056 q^{11} - 3456 q^{12} + 9046 q^{13} - 5376 q^{14} - 532480 q^{16} - 20668 q^{17} + 70436 q^{19} + 27270 q^{21} + 8032 q^{22} - 72856 q^{23} - 1898918 q^{25} + 113312 q^{26} + 78732 q^{27} + 3328 q^{28} + 346972 q^{29} + 98412 q^{31} - 34612 q^{35} - 6065280 q^{36} + 291222 q^{37} + 353888 q^{38} - 694494 q^{39} - 512000 q^{40} + 1103092 q^{41} - 1698798 q^{43} + 193792 q^{44} + 215200 q^{46} - 2376888 q^{47} - 221184 q^{48} + 748490 q^{49} + 1102976 q^{50} - 484380 q^{51} + 928384 q^{52} - 2312916 q^{53} - 677708 q^{55} - 1038336 q^{56} - 540 q^{57} + 3739008 q^{58} + 1361488 q^{59} - 1496596 q^{61} - 2589280 q^{62} - 937494 q^{63} + 68157440 q^{64} - 4730468 q^{65} - 4599936 q^{66} - 4314976 q^{67} - 1322752 q^{68} - 7282008 q^{69} - 13293568 q^{70} + 2207420 q^{71} - 5884178 q^{73} - 746784 q^{74} - 3076002 q^{75} - 2253952 q^{76} + 40881764 q^{77} - 494208 q^{78} - 16138848 q^{79} + 138174660 q^{81} + 7828864 q^{82} - 48573616 q^{83} - 10001664 q^{84} + 2564560 q^{85} + 6530912 q^{86} - 3411396 q^{87} - 1028096 q^{88} - 2882536 q^{89} + 11664000 q^{90} - 27692504 q^{91} + 9325568 q^{92} - 26298216 q^{93} + 49770368 q^{94} - 21932032 q^{95} - 17801870 q^{97} - 12512448 q^{98} - 4414824 q^{99} + O(q^{100}) \)

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

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