↑

Properties

Label 784.6.i
Level $784$
Weight $6$
Character orbit 784.i
Rep. character $\chi_{784}(177,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $196$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 784.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 1168 204 964
Cusp forms 1072 196 876
Eisenstein series 96 8 88

Trace form

\( 196 q - 19 q^{3} + q^{5} - 7613 q^{9} + O(q^{10}) \) \( 196 q - 19 q^{3} + q^{5} - 7613 q^{9} - 605 q^{11} + 4 q^{13} + 494 q^{15} + q^{17} - 549 q^{19} - 1079 q^{23} - 57613 q^{25} + 12146 q^{27} + 176 q^{29} + 3597 q^{31} + 4231 q^{33} + 10649 q^{37} + 12854 q^{39} + 9644 q^{41} + 4912 q^{43} - 106 q^{45} + 38403 q^{47} + 69217 q^{51} + 15973 q^{53} - 42166 q^{55} - 70198 q^{57} - 69899 q^{59} + 6285 q^{61} + 242 q^{65} + 90031 q^{67} + 21022 q^{69} - 435264 q^{71} - 19715 q^{73} - 165612 q^{75} - 58751 q^{79} - 639162 q^{81} - 20792 q^{83} - 205330 q^{85} + 156266 q^{87} - 49539 q^{89} + 73397 q^{93} - 338433 q^{95} - 213460 q^{97} + 758468 q^{99} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)