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Properties

Label 1512.2.cz
Level $1512$
Weight $2$
Character orbit 1512.cz
Rep. character $\chi_{1512}(19,\cdot)$
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.cz (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

\( 184 q - q^{2} + q^{4} + 8 q^{8} + O(q^{10}) \) \( 184 q - q^{2} + q^{4} + 8 q^{8} - 6 q^{10} + 4 q^{11} - 5 q^{14} + q^{16} + 12 q^{17} - 12 q^{19} + 24 q^{20} - 6 q^{22} + 148 q^{25} - 21 q^{32} + 6 q^{34} + 18 q^{35} - 4 q^{43} + 21 q^{44} + 2 q^{46} - 2 q^{49} - 19 q^{50} + 20 q^{56} - 10 q^{58} + 6 q^{59} - 8 q^{64} + 18 q^{65} + 2 q^{67} - 24 q^{70} - 12 q^{73} + 94 q^{74} + 12 q^{76} + 63 q^{80} - 12 q^{82} + 60 q^{83} - 62 q^{86} - 18 q^{88} + 36 q^{89} + 20 q^{91} + 32 q^{92} - 3 q^{94} - 27 q^{98} + O(q^{100}) \)

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

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