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Properties

Label 1512.2.cy
Level $1512$
Weight $2$
Character orbit 1512.cy
Rep. character $\chi_{1512}(179,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $184$
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.cy (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 504 \)
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 600 200 400
Cusp forms 552 184 368
Eisenstein series 48 16 32

Trace form

\( 184 q + 3 q^{2} + q^{4} + O(q^{10}) \) \( 184 q + 3 q^{2} + q^{4} - 6 q^{10} + 3 q^{14} + q^{16} - 4 q^{19} + 6 q^{20} + 2 q^{22} + 148 q^{25} - 6 q^{26} + 33 q^{32} - 4 q^{34} + 30 q^{35} - 12 q^{40} + 12 q^{41} - 4 q^{43} + 9 q^{44} - 6 q^{46} - 2 q^{49} + 21 q^{50} - 18 q^{52} - 18 q^{56} + 6 q^{58} + 6 q^{59} - 8 q^{64} + 6 q^{65} + 2 q^{67} - 18 q^{70} - 4 q^{73} + 2 q^{76} + 87 q^{80} - 4 q^{82} + 72 q^{83} + 14 q^{88} - 24 q^{89} - 36 q^{91} + 36 q^{92} + 9 q^{94} - 4 q^{97} + 57 q^{98} + O(q^{100}) \)

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

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