↑

Properties

Label 2304.4.bd
Level $2304$
Weight $4$
Character orbit 2304.bd
Rep. character $\chi_{2304}(145,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $952$
Sturm bound $1536$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2304.bd (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2304, [\chi])\).

Total New Old
Modular forms 9344 968 8376
Cusp forms 9088 952 8136
Eisenstein series 256 16 240

Trace form

\( 952 q + 8 q^{5} + 8 q^{7} + O(q^{10}) \) \( 952 q + 8 q^{5} + 8 q^{7} - 8 q^{11} - 8 q^{13} + 8 q^{17} + 8 q^{19} - 8 q^{23} - 8 q^{25} + 8 q^{29} - 8 q^{35} - 8 q^{37} + 8 q^{41} + 8 q^{43} - 8 q^{47} - 8 q^{49} + 8 q^{53} + 584 q^{55} + 2744 q^{59} - 8 q^{61} + 16 q^{65} + 824 q^{67} + 440 q^{71} - 8 q^{73} + 8 q^{77} + 5672 q^{79} - 8 q^{83} - 8 q^{85} + 8 q^{89} + 8 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)