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Properties

Label 1512.2.cq
Level $1512$
Weight $2$
Character orbit 1512.cq
Rep. character $\chi_{1512}(37,\cdot)$
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.cq (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

\( 184 q + 2 q^{2} - 2 q^{4} - 2 q^{7} + 8 q^{8} + O(q^{10}) \) \( 184 q + 2 q^{2} - 2 q^{4} - 2 q^{7} + 8 q^{8} + 2 q^{10} + 4 q^{14} - 2 q^{16} + 4 q^{17} - 6 q^{20} + 2 q^{22} - 2 q^{23} + 78 q^{25} + 4 q^{26} - 8 q^{28} - 4 q^{31} + 2 q^{32} + 5 q^{38} - 4 q^{40} + 4 q^{41} - 17 q^{44} - 6 q^{46} + 84 q^{47} - 2 q^{49} + 31 q^{50} + 9 q^{52} + 4 q^{55} + 16 q^{56} + 5 q^{58} - 32 q^{62} - 8 q^{64} + 44 q^{65} + 12 q^{68} + 5 q^{70} + 16 q^{71} - 4 q^{73} - 19 q^{74} - 6 q^{76} - 4 q^{79} + 11 q^{80} + 23 q^{86} - 7 q^{88} - 4 q^{89} + 48 q^{92} - 18 q^{94} + 44 q^{95} - 4 q^{97} + 83 q^{98} + O(q^{100}) \)

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

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