↑

Properties

Label 320.4.be
Level $320$
Weight $4$
Character orbit 320.be
Rep. character $\chi_{320}(21,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $768$
Sturm bound $192$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 320.be (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(320, [\chi])\).

Total New Old
Modular forms 1168 768 400
Cusp forms 1136 768 368
Eisenstein series 32 0 32

Trace form

\( 768 q + O(q^{10}) \) \( 768 q - 944 q^{22} - 2000 q^{24} + 1520 q^{28} + 2480 q^{32} + 2000 q^{34} - 880 q^{38} - 6320 q^{42} - 2000 q^{44} - 2976 q^{51} + 6624 q^{52} + 1728 q^{54} - 112 q^{56} - 4752 q^{58} + 2752 q^{59} - 5856 q^{62} + 10080 q^{63} - 6048 q^{64} - 5472 q^{66} + 8160 q^{67} - 4128 q^{68} + 448 q^{71} + 1296 q^{72} + 752 q^{74} + 5952 q^{76} + 3984 q^{78} - 5664 q^{79} - 9280 q^{80} - 4144 q^{84} + 1040 q^{86} + 6240 q^{88} + 9360 q^{90} + 1488 q^{94} + 25840 q^{96} + 24208 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)