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Properties

Label 320.6.n
Level $320$
Weight $6$
Character orbit 320.n
Rep. character $\chi_{320}(63,\cdot)$
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.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
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 504 124 380
Cusp forms 456 116 340
Eisenstein series 48 8 40

Trace form

\( 116 q + 4 q^{5} + O(q^{10}) \) \( 116 q + 4 q^{5} + 4 q^{13} - 812 q^{17} + 8 q^{21} + 6228 q^{25} + 968 q^{33} + 4 q^{37} - 8 q^{41} - 12496 q^{45} - 77708 q^{53} - 976 q^{57} - 96152 q^{61} + 35364 q^{65} + 10068 q^{73} - 308232 q^{77} - 371772 q^{81} + 31636 q^{85} + 364744 q^{93} - 103548 q^{97} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)