↑

Properties

Label 768.4.s
Level $768$
Weight $4$
Character orbit 768.s
Rep. character $\chi_{768}(47,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $752$
Sturm bound $512$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 768.s (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 192 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(768, [\chi])\).

Total New Old
Modular forms 3136 784 2352
Cusp forms 3008 752 2256
Eisenstein series 128 32 96

Trace form

\( 752 q + 8 q^{3} + 16 q^{7} - 8 q^{9} + O(q^{10}) \) \( 752 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} + 8 q^{15} + 16 q^{19} - 8 q^{21} - 16 q^{25} + 8 q^{27} + 32 q^{31} - 16 q^{37} + 8 q^{39} + 16 q^{43} - 8 q^{45} - 16 q^{49} + 8 q^{51} + 592 q^{55} - 8 q^{57} - 16 q^{61} - 6512 q^{67} - 8 q^{69} - 16 q^{73} + 8 q^{75} + 5680 q^{79} - 8 q^{81} - 16 q^{85} + 8 q^{87} + 16 q^{91} - 224 q^{93} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(768, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(768, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(768, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)