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Properties

Label 320.10.q
Level $320$
Weight $10$
Character orbit 320.q
Rep. character $\chi_{320}(49,\cdot)$
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.q (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

\( 212 q - 2 q^{5} + O(q^{10}) \) \( 212 q - 2 q^{5} + 4 q^{11} + 4 q^{15} - 480884 q^{19} - 78736 q^{21} - 4 q^{29} - 22164496 q^{31} - 15214056 q^{35} + 3945614 q^{45} + 1083782580 q^{49} - 90093056 q^{51} + 144037620 q^{59} - 90121108 q^{61} - 62806092 q^{65} - 382438912 q^{69} - 119613476 q^{75} - 423438896 q^{79} - 7748409788 q^{81} + 3906248 q^{85} - 1231623152 q^{91} + 2480993260 q^{95} - 771348172 q^{99} + O(q^{100}) \)

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

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