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Properties

Label 2112.2.db
Level $2112$
Weight $2$
Character orbit 2112.db
Rep. character $\chi_{2112}(29,\cdot)$
Character field $\Q(\zeta_{80})$
Dimension $12160$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2112 = 2^{6} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2112.db (of order \(80\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2112 \)
Character field: \(\Q(\zeta_{80})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2112, [\chi])\).

Total New Old
Modular forms 12416 12416 0
Cusp forms 12160 12160 0
Eisenstein series 256 256 0

Trace form

\( 12160 q - 24 q^{3} - 48 q^{4} - 40 q^{6} - 80 q^{7} - 24 q^{9} + O(q^{10}) \) \( 12160 q - 24 q^{3} - 48 q^{4} - 40 q^{6} - 80 q^{7} - 24 q^{9} - 64 q^{12} - 80 q^{13} - 24 q^{15} - 48 q^{16} - 40 q^{18} - 80 q^{19} - 64 q^{22} - 40 q^{24} - 48 q^{25} - 24 q^{27} - 80 q^{28} - 40 q^{30} - 128 q^{34} - 24 q^{36} - 48 q^{37} - 40 q^{39} - 80 q^{40} - 24 q^{42} - 64 q^{45} - 80 q^{46} - 24 q^{48} - 48 q^{49} - 40 q^{51} - 80 q^{52} - 40 q^{57} - 48 q^{58} - 24 q^{60} - 80 q^{61} - 80 q^{63} - 336 q^{64} - 48 q^{66} - 384 q^{67} - 24 q^{69} - 144 q^{70} - 40 q^{72} - 80 q^{73} - 24 q^{75} - 64 q^{78} - 80 q^{79} - 24 q^{81} - 48 q^{82} - 40 q^{84} - 80 q^{85} - 144 q^{88} - 40 q^{90} - 48 q^{91} - 72 q^{93} - 80 q^{94} - 40 q^{96} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2112, [\chi])\) into newform subspaces

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