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Properties

Label 2184.2.df
Level $2184$
Weight $2$
Character orbit 2184.df
Rep. character $\chi_{2184}(859,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $384$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 2184 = 2^{3} \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2184.df (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2184, [\chi])\).

Total New Old
Modular forms 912 384 528
Cusp forms 880 384 496
Eisenstein series 32 0 32

Trace form

\( 384 q + 4 q^{2} + 4 q^{4} - 32 q^{8} + 192 q^{9} + O(q^{10}) \) \( 384 q + 4 q^{2} + 4 q^{4} - 32 q^{8} + 192 q^{9} + 36 q^{10} - 16 q^{11} - 12 q^{14} + 4 q^{16} - 4 q^{18} + 16 q^{22} - 192 q^{25} + 20 q^{28} + 16 q^{30} + 4 q^{32} + 48 q^{35} + 8 q^{36} + 36 q^{38} + 32 q^{43} - 32 q^{44} + 24 q^{46} - 80 q^{50} - 56 q^{56} - 12 q^{58} - 80 q^{64} + 72 q^{66} + 64 q^{67} - 132 q^{68} + 76 q^{70} - 16 q^{72} + 68 q^{74} + 36 q^{80} - 192 q^{81} + 72 q^{82} - 32 q^{84} - 116 q^{86} + 4 q^{88} + 112 q^{92} + 72 q^{94} - 24 q^{98} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2184, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2184, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2184, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)