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Properties

Label 1512.2.eb
Level $1512$
Weight $2$
Character orbit 1512.eb
Rep. character $\chi_{1512}(347,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1704$
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.eb (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1512 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1752 1752 0
Cusp forms 1704 1704 0
Eisenstein series 48 48 0

Trace form

\( 1704 q - 3 q^{2} - 6 q^{3} - 3 q^{4} - 12 q^{6} - 18 q^{8} - 6 q^{9} + O(q^{10}) \) \( 1704 q - 3 q^{2} - 6 q^{3} - 3 q^{4} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 6 q^{11} - 3 q^{12} - 36 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} + 6 q^{19} - 12 q^{20} - 12 q^{22} + 66 q^{24} - 6 q^{25} - 24 q^{27} - 12 q^{28} + 15 q^{30} + 57 q^{32} - 6 q^{33} - 6 q^{34} - 18 q^{35} + 18 q^{36} - 51 q^{38} + 27 q^{40} - 24 q^{41} - 21 q^{42} - 24 q^{43} - 6 q^{46} + 54 q^{48} - 12 q^{49} + 3 q^{50} - 42 q^{51} - 3 q^{52} + 39 q^{54} + 57 q^{56} - 42 q^{57} - 3 q^{58} - 6 q^{59} - 63 q^{60} - 117 q^{62} - 6 q^{64} - 6 q^{65} - 3 q^{66} - 6 q^{67} - 42 q^{68} - 33 q^{70} - 9 q^{72} - 12 q^{73} + 63 q^{74} - 6 q^{75} - 24 q^{76} - 30 q^{78} - 6 q^{81} - 6 q^{82} + 36 q^{83} - 21 q^{84} - 117 q^{86} + 21 q^{88} - 18 q^{89} - 39 q^{90} - 6 q^{91} - 72 q^{92} - 3 q^{94} + 213 q^{96} - 24 q^{97} - 180 q^{98} - 24 q^{99} + O(q^{100}) \)

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.