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Properties

Label 1248.2.cd
Level $1248$
Weight $2$
Character orbit 1248.cd
Rep. character $\chi_{1248}(815,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $104$
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.cd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 312 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 480 120 360
Cusp forms 416 104 312
Eisenstein series 64 16 48

Trace form

\( 104 q + 2 q^{3} - 2 q^{9} + O(q^{10}) \) \( 104 q + 2 q^{3} - 2 q^{9} + 4 q^{19} + 56 q^{25} + 32 q^{27} - 14 q^{33} - 12 q^{43} + 32 q^{49} + 20 q^{51} + 4 q^{57} + 4 q^{67} - 32 q^{73} + 18 q^{75} - 2 q^{81} + 12 q^{91} - 12 q^{97} + 172 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1248, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)