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Properties

Label 320.6.j
Level $320$
Weight $6$
Character orbit 320.j
Rep. character $\chi_{320}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $116$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(320, [\chi])\).

Total New Old
Modular forms 496 124 372
Cusp forms 464 116 348
Eisenstein series 32 8 24

Trace form

\( 116 q - 2 q^{5} + 4 q^{7} - 8748 q^{9} + O(q^{10}) \) \( 116 q - 2 q^{5} + 4 q^{7} - 8748 q^{9} + 4 q^{11} - 4 q^{13} - 972 q^{15} - 4 q^{17} + 2360 q^{19} - 4 q^{21} + 4 q^{23} - 4 q^{33} + 8640 q^{35} - 4 q^{37} + 1316 q^{43} - 5766 q^{45} - 65256 q^{47} - 10436 q^{51} + 4 q^{55} + 972 q^{57} + 14480 q^{59} + 48076 q^{61} - 972 q^{63} - 4 q^{65} + 89260 q^{67} - 21348 q^{69} + 143848 q^{71} - 10072 q^{73} + 32272 q^{75} + 551116 q^{81} - 6252 q^{85} + 282188 q^{87} + 164724 q^{91} + 968 q^{93} - 204760 q^{95} - 4 q^{97} + 168788 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)