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Properties

Label 2448.2.da
Level $2448$
Weight $2$
Character orbit 2448.da
Rep. character $\chi_{2448}(443,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1536$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2448.da (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2448, [\chi])\).

Total New Old
Modular forms 1744 1536 208
Cusp forms 1712 1536 176
Eisenstein series 32 0 32

Trace form

\( 1536 q - 12 q^{6} + O(q^{10}) \) \( 1536 q - 12 q^{6} + 24 q^{12} + 84 q^{20} + 32 q^{24} + 24 q^{27} + 48 q^{30} + 8 q^{36} + 48 q^{39} - 40 q^{42} - 40 q^{48} - 768 q^{49} + 68 q^{54} - 36 q^{58} + 72 q^{59} - 124 q^{60} + 72 q^{64} - 104 q^{66} + 112 q^{75} + 64 q^{78} + 72 q^{82} - 296 q^{84} - 60 q^{86} - 112 q^{87} - 48 q^{88} - 72 q^{90} + 48 q^{93} + 176 q^{96} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2448, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2448, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)