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Properties

Label 784.6.u
Level $784$
Weight $6$
Character orbit 784.u
Rep. character $\chi_{784}(113,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $834$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 784.u (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 3396 846 2550
Cusp forms 3324 834 2490
Eisenstein series 72 12 60

Trace form

\( 834 q + 23 q^{3} - 5 q^{5} - 56 q^{7} - 11102 q^{9} + O(q^{10}) \) \( 834 q + 23 q^{3} - 5 q^{5} - 56 q^{7} - 11102 q^{9} + 5 q^{11} - 5 q^{13} - 481 q^{15} - 5 q^{17} - 9748 q^{19} - 583 q^{21} - 3823 q^{23} - 87108 q^{25} + 5351 q^{27} - 19905 q^{29} + 30272 q^{31} + 9913 q^{33} - 10319 q^{35} - 5 q^{37} - 54571 q^{39} - 9645 q^{41} - 36971 q^{43} + 18531 q^{45} + 10543 q^{47} + 22886 q^{49} - 8661 q^{51} - 17517 q^{53} - 30433 q^{55} - 14108 q^{57} + 48183 q^{59} + 12563 q^{61} + 165412 q^{63} + 48445 q^{65} + 118916 q^{67} + 137601 q^{69} - 179795 q^{71} - 59141 q^{73} + 493129 q^{75} + 54213 q^{77} + 75752 q^{79} - 971110 q^{81} + 392799 q^{83} + 6245 q^{85} + 40055 q^{87} + 44795 q^{89} + 325829 q^{91} + 146796 q^{93} - 409626 q^{95} - 7612 q^{97} - 302568 q^{99} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)