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Properties

Label 1512.2.cs
Level $1512$
Weight $2$
Character orbit 1512.cs
Rep. character $\chi_{1512}(253,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.cs (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1512, [\chi])\).

Total New Old
Modular forms 600 144 456
Cusp forms 552 144 408
Eisenstein series 48 0 48

Trace form

\( 144 q - 12 q^{8} + O(q^{10}) \) \( 144 q - 12 q^{8} - 14 q^{20} - 24 q^{23} + 72 q^{25} + 56 q^{26} + 10 q^{32} + 12 q^{34} + 28 q^{38} + 12 q^{40} + 8 q^{41} + 64 q^{44} + 24 q^{46} - 72 q^{49} - 46 q^{50} - 18 q^{52} + 18 q^{58} - 48 q^{62} - 60 q^{64} - 78 q^{68} + 112 q^{71} - 12 q^{76} - 88 q^{80} - 36 q^{82} + 42 q^{86} - 24 q^{88} - 66 q^{92} + 6 q^{94} + 64 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1512, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1512, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)