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Properties

Label 1248.2.ee
Level $1248$
Weight $2$
Character orbit 1248.ee
Rep. character $\chi_{1248}(19,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $896$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1248.ee (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 416 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1248, [\chi])\).

Total New Old
Modular forms 1824 896 928
Cusp forms 1760 896 864
Eisenstein series 64 0 64

Trace form

\( 896 q + O(q^{10}) \) \( 896 q + 64 q^{14} + 64 q^{20} - 88 q^{22} - 128 q^{28} - 16 q^{30} - 80 q^{32} + 40 q^{34} + 120 q^{42} - 32 q^{43} + 32 q^{44} + 48 q^{46} + 448 q^{49} - 80 q^{50} - 32 q^{55} + 64 q^{59} - 48 q^{60} - 72 q^{62} - 48 q^{68} - 200 q^{70} + 128 q^{71} + 80 q^{83} + 16 q^{88} + 32 q^{90} + 48 q^{91} + 24 q^{94} + 72 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1248, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1248, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1248, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)