↑

Properties

Label 3072.2.bi
Level $3072$
Weight $2$
Character orbit 3072.bi
Rep. character $\chi_{3072}(11,\cdot)$
Character field $\Q(\zeta_{256})$
Dimension $65280$
Sturm bound $1024$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3072 = 2^{10} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3072.bi (of order \(256\) and degree \(128\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3072 \)
Character field: \(\Q(\zeta_{256})\)
Sturm bound: \(1024\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3072, [\chi])\).

Total New Old
Modular forms 65792 65792 0
Cusp forms 65280 65280 0
Eisenstein series 512 512 0

Trace form

\( 65280 q - 128 q^{3} - 256 q^{4} - 128 q^{6} - 256 q^{7} - 128 q^{9} + O(q^{10}) \) \( 65280 q - 128 q^{3} - 256 q^{4} - 128 q^{6} - 256 q^{7} - 128 q^{9} - 256 q^{10} - 128 q^{12} - 256 q^{13} - 128 q^{15} - 256 q^{16} - 128 q^{18} - 256 q^{19} - 128 q^{21} - 256 q^{22} - 128 q^{24} - 256 q^{25} - 128 q^{27} - 256 q^{28} - 128 q^{30} - 256 q^{31} - 128 q^{33} - 256 q^{34} - 128 q^{36} - 256 q^{37} - 128 q^{39} - 256 q^{40} - 128 q^{42} - 256 q^{43} - 128 q^{45} - 256 q^{46} - 128 q^{48} - 256 q^{49} - 128 q^{51} - 256 q^{52} - 128 q^{54} - 256 q^{55} - 128 q^{57} - 256 q^{58} - 128 q^{60} - 256 q^{61} - 128 q^{63} - 256 q^{64} - 128 q^{66} - 256 q^{67} - 128 q^{69} - 256 q^{70} - 128 q^{72} - 256 q^{73} - 128 q^{75} - 256 q^{76} - 128 q^{78} - 256 q^{79} - 128 q^{81} - 256 q^{82} - 128 q^{84} - 256 q^{85} - 128 q^{87} - 256 q^{88} - 128 q^{90} - 256 q^{91} - 128 q^{93} - 256 q^{94} - 128 q^{96} - 256 q^{97} - 128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3072, [\chi])\) into newform subspaces

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