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Properties

Label 1512.2.dn
Level $1512$
Weight $2$
Character orbit 1512.dn
Rep. character $\chi_{1512}(173,\cdot)$
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.dn (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

\( 1704 q - 3 q^{2} - 3 q^{4} - 12 q^{7} - 18 q^{8} - 6 q^{9} + O(q^{10}) \) \( 1704 q - 3 q^{2} - 3 q^{4} - 12 q^{7} - 18 q^{8} - 6 q^{9} - 9 q^{10} - 9 q^{12} + 24 q^{14} - 24 q^{15} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{22} - 6 q^{23} + 18 q^{24} - 6 q^{25} - 12 q^{28} + 15 q^{30} - 18 q^{31} + 57 q^{32} - 18 q^{33} + 18 q^{34} - 42 q^{36} - 9 q^{38} - 6 q^{39} - 9 q^{40} - 21 q^{42} - 6 q^{46} - 18 q^{47} - 12 q^{49} - 27 q^{50} - 9 q^{52} + 117 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} + 57 q^{60} + 99 q^{62} + 48 q^{63} - 6 q^{64} - 6 q^{65} - 9 q^{66} - 54 q^{68} - 21 q^{70} - 36 q^{71} - 9 q^{72} - 21 q^{74} + 36 q^{76} - 30 q^{78} - 6 q^{79} - 6 q^{81} - 18 q^{82} + 27 q^{84} - 117 q^{86} - 18 q^{87} - 27 q^{88} - 18 q^{89} - 81 q^{90} - 72 q^{92} - 9 q^{94} + 54 q^{95} - 9 q^{96} + 162 q^{98} + O(q^{100}) \)

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.