Properties

Label 1512.2.dn
Level 1512
Weight 2
Character orbit 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

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

Decomposition of \(S_{2}^{\mathrm{new}}(1512, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database