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Properties

Label 784.6.w
Level $784$
Weight $6$
Character orbit 784.w
Rep. character $\chi_{784}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1584$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 784.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(784, [\chi])\).

Total New Old
Modular forms 2272 1616 656
Cusp forms 2208 1584 624
Eisenstein series 64 32 32

Trace form

\( 1584 q + 2 q^{2} + 6 q^{3} - 42 q^{4} + 6 q^{5} - 508 q^{8} + O(q^{10}) \) \( 1584 q + 2 q^{2} + 6 q^{3} - 42 q^{4} + 6 q^{5} - 508 q^{8} - 1596 q^{10} + 1210 q^{11} + 6 q^{12} - 4178 q^{16} + 12 q^{17} - 5884 q^{18} + 6 q^{19} - 3552 q^{22} + 3348 q^{23} + 6 q^{24} + 6 q^{26} + 16272 q^{29} + 32378 q^{30} - 1908 q^{32} + 12 q^{33} + 66400 q^{36} + 21298 q^{37} + 6 q^{38} + 4 q^{39} + 88866 q^{40} - 64160 q^{43} + 9680 q^{44} - 1452 q^{45} + 25268 q^{46} + 103644 q^{50} + 6238 q^{51} - 19452 q^{52} + 49458 q^{53} - 184758 q^{54} + 72860 q^{58} - 43434 q^{59} + 48286 q^{60} + 6 q^{61} + 323292 q^{64} + 4 q^{65} + 106506 q^{66} - 105786 q^{67} + 38736 q^{68} - 287712 q^{71} + 68550 q^{72} - 22564 q^{74} - 18744 q^{75} - 953068 q^{78} - 370092 q^{80} + 4776412 q^{81} + 377538 q^{82} + 12484 q^{85} + 500910 q^{86} + 12 q^{87} - 143640 q^{88} + 427708 q^{92} + 1946 q^{93} + 390930 q^{94} - 1208292 q^{96} + 1215632 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(784, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(784, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)