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Properties

Label 546.8.j
Level $546$
Weight $8$
Character orbit 546.j
Rep. character $\chi_{546}(289,\cdot)$
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.j (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

\( 260 q - 54 q^{3} + 16640 q^{4} + 1234 q^{7} - 94770 q^{9} + O(q^{10}) \) \( 260 q - 54 q^{3} + 16640 q^{4} + 1234 q^{7} - 94770 q^{9} - 8000 q^{10} + 3028 q^{11} - 3456 q^{12} + 9046 q^{13} - 5376 q^{14} + 1064960 q^{16} + 41336 q^{17} - 35218 q^{19} + 27270 q^{21} + 8032 q^{22} + 145712 q^{23} - 1898918 q^{25} + 113312 q^{26} + 78732 q^{27} + 78976 q^{28} + 346972 q^{29} + 98412 q^{31} + 659888 q^{35} - 6065280 q^{36} - 582444 q^{37} + 353888 q^{38} + 41472 q^{39} - 512000 q^{40} + 1103092 q^{41} - 1698798 q^{43} + 193792 q^{44} - 430400 q^{46} - 2376888 q^{47} - 221184 q^{48} - 3434098 q^{49} + 1102976 q^{50} - 484380 q^{51} + 578944 q^{52} - 2312916 q^{53} - 677708 q^{55} - 344064 q^{56} - 540 q^{57} - 1869504 q^{58} - 2722976 q^{59} + 748298 q^{61} - 2589280 q^{62} + 37908 q^{63} + 68157440 q^{64} + 3997792 q^{65} - 4599936 q^{66} + 2157488 q^{67} + 2645504 q^{68} - 7282008 q^{69} - 13293568 q^{70} + 2207420 q^{71} - 5884178 q^{73} + 1493568 q^{74} + 6152004 q^{75} - 2253952 q^{76} + 40881764 q^{77} - 494208 q^{78} - 16138848 q^{79} - 69087330 q^{81} - 3914432 q^{82} - 48573616 q^{83} + 1745280 q^{84} + 2564560 q^{85} + 6530912 q^{86} + 6822792 q^{87} + 514048 q^{88} + 5765072 q^{89} + 11664000 q^{90} + 24367084 q^{91} + 9325568 q^{92} + 52596432 q^{93} - 24885184 q^{94} + 43864064 q^{95} - 17801870 q^{97} - 5765952 q^{98} - 4414824 q^{99} + O(q^{100}) \)

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

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