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Properties

Label 1536.2.be
Level $1536$
Weight $2$
Character orbit 1536.be
Rep. character $\chi_{1536}(11,\cdot)$
Character field $\Q(\zeta_{128})$
Dimension $16256$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 1536 = 2^{9} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1536.be (of order \(128\) and degree \(64\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1536 \)
Character field: \(\Q(\zeta_{128})\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1536, [\chi])\).

Total New Old
Modular forms 16512 16512 0
Cusp forms 16256 16256 0
Eisenstein series 256 256 0

Trace form

\( 16256 q - 64 q^{3} - 128 q^{4} - 64 q^{6} - 128 q^{7} - 64 q^{9} + O(q^{10}) \) \( 16256 q - 64 q^{3} - 128 q^{4} - 64 q^{6} - 128 q^{7} - 64 q^{9} - 128 q^{10} - 64 q^{12} - 128 q^{13} - 64 q^{15} - 128 q^{16} - 64 q^{18} - 128 q^{19} - 64 q^{21} - 128 q^{22} - 64 q^{24} - 128 q^{25} - 64 q^{27} - 128 q^{28} - 64 q^{30} - 128 q^{31} - 64 q^{33} - 128 q^{34} - 64 q^{36} - 128 q^{37} - 64 q^{39} - 128 q^{40} - 64 q^{42} - 128 q^{43} - 64 q^{45} - 128 q^{46} - 64 q^{48} - 128 q^{49} - 64 q^{51} - 128 q^{52} - 64 q^{54} - 128 q^{55} - 64 q^{57} - 128 q^{58} - 64 q^{60} - 128 q^{61} - 64 q^{63} - 128 q^{64} - 64 q^{66} - 128 q^{67} - 64 q^{69} - 128 q^{70} - 64 q^{72} - 128 q^{73} - 64 q^{75} - 128 q^{76} - 64 q^{78} - 128 q^{79} - 64 q^{81} - 128 q^{82} - 64 q^{84} - 128 q^{85} - 64 q^{87} - 128 q^{88} - 64 q^{90} - 128 q^{91} - 64 q^{93} - 128 q^{94} - 64 q^{96} - 128 q^{97} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1536, [\chi])\) into newform subspaces

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