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Properties

Label 784.4.u
Level $784$
Weight $4$
Character orbit 784.u
Rep. character $\chi_{784}(113,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $498$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.u (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(784, [\chi])\).

Total New Old
Modular forms 2052 510 1542
Cusp forms 1980 498 1482
Eisenstein series 72 12 60

Trace form

\( 498 q - q^{3} - 5 q^{5} + 24 q^{7} - 734 q^{9} + O(q^{10}) \) \( 498 q - q^{3} - 5 q^{5} + 24 q^{7} - 734 q^{9} + 5 q^{11} - 5 q^{13} - 49 q^{15} - 5 q^{17} + 876 q^{19} + 89 q^{21} - 79 q^{23} - 1812 q^{25} - 265 q^{27} + 135 q^{29} - 1344 q^{31} + 25 q^{33} + 169 q^{35} - 5 q^{37} - 1099 q^{39} + 291 q^{41} + 341 q^{43} - 141 q^{45} + 271 q^{47} - 338 q^{49} + 651 q^{51} + 387 q^{53} + 1263 q^{55} - 308 q^{57} - 369 q^{59} + 195 q^{61} - 5108 q^{63} - 35 q^{65} - 156 q^{67} - 3567 q^{69} - 275 q^{71} - 773 q^{73} - 359 q^{75} + 573 q^{77} - 1752 q^{79} - 4486 q^{81} - 633 q^{83} + 245 q^{85} - 1561 q^{87} - 1285 q^{89} - 5219 q^{91} - 252 q^{93} + 462 q^{95} + 36 q^{97} - 2760 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(784, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(784, [\chi])\) into lower level spaces

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