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Properties

Label 320.10.n
Level $320$
Weight $10$
Character orbit 320.n
Rep. character $\chi_{320}(63,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $212$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 320.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(320, [\chi])\).

Total New Old
Modular forms 888 220 668
Cusp forms 840 212 628
Eisenstein series 48 8 40

Trace form

\( 212 q + 4 q^{5} + O(q^{10}) \) \( 212 q + 4 q^{5} + 4 q^{13} + 407988 q^{17} + 8 q^{21} - 3443532 q^{25} + 78728 q^{33} + 4 q^{37} - 8 q^{41} - 7812496 q^{45} - 322945868 q^{53} - 78736 q^{57} - 180242200 q^{61} - 287601596 q^{65} + 241709748 q^{73} - 1038875592 q^{77} - 7001923740 q^{81} + 2616531796 q^{85} - 2698944056 q^{93} - 2752258268 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)