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Properties

Label 900.6.bj
Level $900$
Weight $6$
Character orbit 900.bj
Rep. character $\chi_{900}(127,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2984$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 900.bj (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(900, [\chi])\).

Total New Old
Modular forms 7264 3016 4248
Cusp forms 7136 2984 4152
Eisenstein series 128 32 96

Trace form

\( 2984 q + 8 q^{2} - 10 q^{4} + 16 q^{5} - 238 q^{8} + O(q^{10}) \) \( 2984 q + 8 q^{2} - 10 q^{4} + 16 q^{5} - 238 q^{8} + 560 q^{10} - 138 q^{13} + 10 q^{14} - 6 q^{16} - 994 q^{17} + 5466 q^{20} - 3154 q^{22} + 7774 q^{25} + 16 q^{26} + 16502 q^{28} + 20 q^{29} - 7962 q^{32} - 10 q^{34} + 1866 q^{37} + 56356 q^{38} - 78220 q^{40} + 12 q^{41} - 51720 q^{44} - 6 q^{46} + 220970 q^{50} + 108948 q^{52} - 18718 q^{53} + 6 q^{56} - 358904 q^{58} - 12 q^{61} + 23024 q^{62} + 345620 q^{64} + 20242 q^{65} - 32258 q^{68} - 16906 q^{70} - 26182 q^{73} + 4080 q^{76} + 187748 q^{77} + 66590 q^{80} + 596502 q^{82} - 50544 q^{85} + 6 q^{86} - 1258642 q^{88} - 1141250 q^{89} + 145646 q^{92} - 192890 q^{94} - 1120766 q^{97} - 915372 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)