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Properties

Label 819.6.fa
Level $819$
Weight $6$
Character orbit 819.fa
Rep. character $\chi_{819}(124,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2224$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 819.fa (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 819 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(819, [\chi])\).

Total New Old
Modular forms 2256 2256 0
Cusp forms 2224 2224 0
Eisenstein series 32 32 0

Trace form

\( 2224 q + 2 q^{2} - 192 q^{6} - 118 q^{7} - 80 q^{8} - 4 q^{9} + O(q^{10}) \) \( 2224 q + 2 q^{2} - 192 q^{6} - 118 q^{7} - 80 q^{8} - 4 q^{9} - 24 q^{10} - 384 q^{11} - 4 q^{14} - 1592 q^{15} - 557052 q^{16} - 12 q^{17} + 1406 q^{18} - 12 q^{19} + 12288 q^{20} + 1998 q^{21} + 4 q^{22} - 6 q^{23} + 7596 q^{24} - 12 q^{26} - 15156 q^{27} - 5448 q^{28} + 2844 q^{29} - 18336 q^{30} - 6 q^{31} - 2558 q^{32} + 57348 q^{33} + 192 q^{34} - 22332 q^{35} - 12 q^{36} - 10320 q^{37} + 308 q^{39} + 40646 q^{42} - 20164 q^{44} - 6 q^{45} + 124 q^{46} - 6 q^{47} - 2916 q^{48} + 19462 q^{50} + 2916 q^{51} + 81792 q^{52} - 5200 q^{53} - 6 q^{54} + 12288 q^{56} - 61466 q^{57} - 132 q^{58} - 6 q^{59} + 7370 q^{60} - 6 q^{61} + 141044 q^{63} + 35716 q^{65} - 12 q^{66} - 2490 q^{67} - 6 q^{68} + 8862 q^{69} - 8680 q^{70} + 35712 q^{71} - 539834 q^{72} - 12 q^{73} + 99650 q^{74} - 6 q^{75} - 384 q^{76} + 78552 q^{77} + 316544 q^{78} - 72056 q^{79} - 885822 q^{80} - 223484 q^{81} - 24 q^{82} - 400016 q^{84} - 30204 q^{85} - 175920 q^{86} + 409482 q^{87} - 6 q^{88} - 12 q^{89} - 708588 q^{90} + 31424 q^{91} + 309172 q^{92} + 68166 q^{93} - 6 q^{94} + 150138 q^{96} + 208074 q^{97} - 1279840 q^{98} + 378928 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(819, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.