↑

Properties

Label 320.10.s
Level $320$
Weight $10$
Character orbit 320.s
Rep. character $\chi_{320}(207,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $212$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 320.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
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 880 220 660
Cusp forms 848 212 636
Eisenstein series 32 8 24

Trace form

\( 212 q + 4 q^{3} - 2 q^{5} + 4 q^{7} + 1338444 q^{9} + O(q^{10}) \) \( 212 q + 4 q^{3} - 2 q^{5} + 4 q^{7} + 1338444 q^{9} + 4 q^{11} + 78732 q^{15} - 4 q^{17} - 480888 q^{19} - 4 q^{21} + 4 q^{23} + 78736 q^{27} - 4 q^{33} + 15214060 q^{35} - 3945618 q^{45} - 112458264 q^{47} + 90014332 q^{51} - 4 q^{53} + 4 q^{55} - 78732 q^{57} + 144037616 q^{59} + 90121100 q^{61} + 78732 q^{63} - 4 q^{65} + 382281444 q^{69} + 238101480 q^{71} + 241709752 q^{73} + 1034969596 q^{75} - 161414432 q^{77} + 7748409772 q^{81} + 795523164 q^{83} + 3906248 q^{85} + 2350951628 q^{87} - 1393037580 q^{91} + 2812876760 q^{95} - 4 q^{97} + 778491244 q^{99} + O(q^{100}) \)

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

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