Properties

Label 2304.2.bd
Level $2304$
Weight $2$
Character orbit 2304.bd
Rep. character $\chi_{2304}(145,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $312$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2304.bd (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2304, [\chi])\).

Total New Old
Modular forms 3200 328 2872
Cusp forms 2944 312 2632
Eisenstein series 256 16 240

Trace form

\( 312q + 8q^{5} + 8q^{7} + O(q^{10}) \) \( 312q + 8q^{5} + 8q^{7} - 8q^{11} - 8q^{13} + 8q^{17} + 8q^{19} - 8q^{23} - 8q^{25} + 8q^{29} - 8q^{35} - 8q^{37} + 8q^{41} + 8q^{43} - 8q^{47} - 8q^{49} + 8q^{53} + 72q^{55} - 72q^{59} - 8q^{61} + 16q^{65} - 8q^{67} - 72q^{71} - 8q^{73} + 8q^{77} + 40q^{79} - 8q^{83} - 8q^{85} + 8q^{89} + 8q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces

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