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Properties

Label 784.6.j
Level $784$
Weight $6$
Character orbit 784.j
Rep. character $\chi_{784}(195,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $792$
Sturm bound $672$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 1136 808 328
Cusp forms 1104 792 312
Eisenstein series 32 16 16

Trace form

\( 792 q + 4 q^{2} + 48 q^{4} + 484 q^{8} + O(q^{10}) \) \( 792 q + 4 q^{2} + 48 q^{4} + 484 q^{8} - 1204 q^{11} + 4184 q^{16} - 6140 q^{18} - 16860 q^{22} - 3336 q^{23} + 8136 q^{29} - 32564 q^{30} - 3816 q^{32} + 27056 q^{36} - 21292 q^{37} + 8 q^{39} - 32080 q^{43} - 78908 q^{44} + 49768 q^{46} - 51168 q^{50} + 18308 q^{51} - 49452 q^{53} - 5420 q^{58} - 31324 q^{60} + 87864 q^{64} + 8 q^{65} - 28092 q^{67} + 287664 q^{71} - 265152 q^{72} - 13796 q^{74} + 44548 q^{78} - 4776400 q^{81} - 12508 q^{85} - 108384 q^{86} + 610860 q^{88} - 299428 q^{92} - 1940 q^{93} + 252064 q^{99} + O(q^{100}) \)

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

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