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Properties

Label 720.6.cf
Level $720$
Weight $6$
Character orbit 720.cf
Rep. character $\chi_{720}(11,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1920$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 720.cf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(720, [\chi])\).

Total New Old
Modular forms 2896 1920 976
Cusp forms 2864 1920 944
Eisenstein series 32 0 32

Trace form

\( 1920 q - 228 q^{6} + O(q^{10}) \) \( 1920 q - 228 q^{6} - 3144 q^{12} - 8020 q^{18} + 30120 q^{24} - 7464 q^{27} - 34428 q^{36} - 89808 q^{39} - 15920 q^{42} - 53880 q^{46} + 94040 q^{48} - 2304960 q^{49} + 16360 q^{51} + 269604 q^{54} + 12996 q^{58} - 91512 q^{59} + 7700 q^{60} - 209592 q^{64} + 215880 q^{66} - 447564 q^{68} - 556528 q^{72} - 597912 q^{74} - 50340 q^{76} + 46276 q^{78} - 604872 q^{82} + 987720 q^{83} + 859708 q^{84} - 71100 q^{90} + 362352 q^{93} - 634732 q^{96} - 169760 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(720, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(720, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)