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Properties

Label 546.8.by
Level $546$
Weight $8$
Character orbit 546.by
Rep. character $\chi_{546}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $520$
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.by (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 520 2648
Cusp forms 3104 520 2584
Eisenstein series 64 0 64

Trace form

\( 520 q + 228 q^{7} - 379080 q^{9} + O(q^{10}) \) \( 520 q + 228 q^{7} - 379080 q^{9} - 6056 q^{11} - 6912 q^{12} + 7232 q^{14} + 1064960 q^{16} + 5708 q^{19} - 67608 q^{21} + 16064 q^{22} + 35840 q^{28} - 162408 q^{29} - 107524 q^{31} + 926000 q^{35} + 456972 q^{37} + 1388988 q^{39} - 5855520 q^{41} + 4477260 q^{43} + 775168 q^{44} - 1235520 q^{46} - 5320196 q^{49} + 2205952 q^{50} - 3488184 q^{51} - 472832 q^{52} + 2800456 q^{53} - 4066248 q^{55} + 3452928 q^{56} - 540 q^{57} + 9209984 q^{58} + 10869696 q^{62} - 166212 q^{63} - 9398072 q^{65} + 4997168 q^{67} + 7936512 q^{68} + 8756608 q^{70} - 14016104 q^{71} - 18420584 q^{73} + 10050496 q^{74} + 11812500 q^{75} - 7352320 q^{76} + 5104512 q^{78} - 11203712 q^{79} + 276349320 q^{81} - 58889472 q^{82} + 19825296 q^{83} - 15634944 q^{84} - 62361608 q^{85} + 24586496 q^{86} + 20468376 q^{87} + 63157152 q^{89} - 61859656 q^{91} + 18651136 q^{92} - 14152428 q^{93} - 20652000 q^{95} + 21473548 q^{97} - 36556800 q^{98} + 4414824 q^{99} + O(q^{100}) \)

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

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