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Properties

Label 819.6.gl
Level $819$
Weight $6$
Character orbit 819.gl
Rep. character $\chi_{819}(34,\cdot)$
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.gl (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

\( 2224 q - 4 q^{2} + 56 q^{7} - 272 q^{8} - 16 q^{9} + O(q^{10}) \) \( 2224 q - 4 q^{2} + 56 q^{7} - 272 q^{8} - 16 q^{9} - 384 q^{11} - 4 q^{14} - 3056 q^{15} + 278520 q^{16} + 4376 q^{18} - 5466 q^{21} - 8 q^{22} - 11400 q^{28} - 5688 q^{29} + 4348 q^{32} + 44640 q^{35} + 20616 q^{37} - 5452 q^{39} + 40784 q^{42} + 40688 q^{44} - 272 q^{46} + 328 q^{50} + 41504 q^{53} - 60008 q^{57} + 252 q^{58} - 7936 q^{60} + 163568 q^{63} - 71432 q^{65} - 2496 q^{67} - 46180 q^{70} - 71472 q^{71} - 421760 q^{72} - 199312 q^{74} - 630196 q^{78} + 144112 q^{79} + 446944 q^{81} + 486406 q^{84} - 30204 q^{85} + 380436 q^{86} - 62872 q^{91} - 642944 q^{92} + 68160 q^{93} - 928288 q^{98} - 15932 q^{99} + O(q^{100}) \)

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.