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Properties

Label 1512.2.br
Level $1512$
Weight $2$
Character orbit 1512.br
Rep. character $\chi_{1512}(827,\cdot)$
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.br (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

\( 144 q + O(q^{10}) \) \( 144 q + 42 q^{20} - 72 q^{25} + 30 q^{32} + 12 q^{34} + 12 q^{40} - 24 q^{41} - 24 q^{46} + 72 q^{49} + 78 q^{50} + 18 q^{52} - 18 q^{58} + 72 q^{59} - 12 q^{64} - 78 q^{68} - 84 q^{74} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} - 42 q^{94} + O(q^{100}) \)

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

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