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Properties

Label 784.4.bg
Level $784$
Weight $4$
Character orbit 784.bg
Rep. character $\chi_{784}(65,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $996$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.bg (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 4104 1020 3084
Cusp forms 3960 996 2964
Eisenstein series 144 24 120

Trace form

\( 996 q + 19 q^{3} - 13 q^{5} - 6 q^{7} + 716 q^{9} + O(q^{10}) \) \( 996 q + 19 q^{3} - 13 q^{5} - 6 q^{7} + 716 q^{9} + 13 q^{11} - 10 q^{13} + 64 q^{15} - 13 q^{17} - 588 q^{19} - 107 q^{21} - 29 q^{23} + 2046 q^{25} - 368 q^{27} - 150 q^{29} + 1002 q^{31} - 79 q^{33} + 371 q^{35} - 13 q^{37} + 1666 q^{39} - 306 q^{41} - 326 q^{43} - 456 q^{45} - 559 q^{47} + 476 q^{49} + 417 q^{51} + 183 q^{53} + 72 q^{55} + 293 q^{57} + 1419 q^{59} + 87 q^{61} + 5096 q^{63} - 28 q^{65} - 78 q^{67} + 504 q^{69} + 290 q^{71} + 1079 q^{73} - 592 q^{75} + 393 q^{77} - 876 q^{79} + 3625 q^{81} - 3834 q^{83} - 260 q^{85} - 2336 q^{87} + 631 q^{89} + 3074 q^{91} + 66 q^{93} - 696 q^{95} + 2304 q^{97} + 2796 q^{99} + O(q^{100}) \)

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

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