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

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

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

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