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Properties

Label 784.6.bg
Level $784$
Weight $6$
Character orbit 784.bg
Rep. character $\chi_{784}(65,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1668$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 784.bg (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 6792 1692 5100
Cusp forms 6648 1668 4980
Eisenstein series 144 24 120

Trace form

\( 1668 q - 5 q^{3} - 13 q^{5} + 74 q^{7} + 11084 q^{9} + O(q^{10}) \) \( 1668 q - 5 q^{3} - 13 q^{5} + 74 q^{7} + 11084 q^{9} + 13 q^{11} - 10 q^{13} + 496 q^{15} - 13 q^{17} + 14620 q^{19} + 565 q^{21} - 1901 q^{23} + 82998 q^{25} + 12160 q^{27} + 19890 q^{29} - 36758 q^{31} + 4217 q^{33} - 14845 q^{35} - 13 q^{37} + 86314 q^{39} + 9630 q^{41} + 36986 q^{43} - 120 q^{45} + 38417 q^{47} - 3764 q^{49} - 3591 q^{51} - 8769 q^{53} - 42152 q^{55} + 14093 q^{57} - 69885 q^{59} + 6271 q^{61} - 44464 q^{63} + 24212 q^{65} + 59458 q^{67} - 200136 q^{69} + 179810 q^{71} - 19729 q^{73} - 755152 q^{75} - 28047 q^{77} + 37876 q^{79} + 1039081 q^{81} - 20778 q^{83} - 6260 q^{85} + 156280 q^{87} - 49553 q^{89} - 590222 q^{91} + 75210 q^{93} - 228240 q^{95} - 213488 q^{97} + 302604 q^{99} + O(q^{100}) \)

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

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