↑

Properties

Label 688.6.u
Level $688$
Weight $6$
Character orbit 688.u
Rep. character $\chi_{688}(97,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $654$
Sturm bound $528$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 688 = 2^{4} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 688.u (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(688, [\chi])\).

Total New Old
Modular forms 2676 666 2010
Cusp forms 2604 654 1950
Eisenstein series 72 12 60

Trace form

\( 654 q + 23 q^{3} - 5 q^{5} + 476 q^{7} - 8628 q^{9} + O(q^{10}) \) \( 654 q + 23 q^{3} - 5 q^{5} + 476 q^{7} - 8628 q^{9} + 609 q^{11} - 5 q^{13} - 481 q^{15} + 999 q^{17} + 5407 q^{19} - 2860 q^{21} - 4659 q^{23} - 65630 q^{25} + 5351 q^{27} + 12027 q^{29} + 10845 q^{31} + 15207 q^{33} - 1158 q^{35} - 10660 q^{37} - 66739 q^{39} - 5809 q^{41} - 26828 q^{43} + 18531 q^{45} + 1259 q^{47} + 1498438 q^{49} + 30731 q^{51} + 61815 q^{53} - 152609 q^{55} - 15299 q^{57} - 36981 q^{59} - 5 q^{61} + 3688 q^{63} + 6245 q^{65} + 300441 q^{67} - 20359 q^{69} - 62845 q^{71} - 106201 q^{73} + 104775 q^{75} - 91488 q^{77} + 429808 q^{79} - 811614 q^{81} - 260425 q^{83} + 6238 q^{85} - 82078 q^{87} - 163673 q^{89} + 268336 q^{91} + 474 q^{93} - 289505 q^{95} + 40767 q^{97} + 126041 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(688, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(688, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(688, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(86, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(172, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(344, [\chi])\)\(^{\oplus 2}\)