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Properties

Label 900.4.bt
Level $900$
Weight $4$
Character orbit 900.bt
Rep. character $\chi_{900}(77,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1440$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 900.bt (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(900, [\chi])\).

Total New Old
Modular forms 8736 1440 7296
Cusp forms 8544 1440 7104
Eisenstein series 192 0 192

Trace form

\( 1440 q - 4 q^{3} + O(q^{10}) \) \( 1440 q - 4 q^{3} + 80 q^{15} + 312 q^{23} - 576 q^{25} + 152 q^{27} - 172 q^{33} - 144 q^{37} + 2440 q^{39} - 2280 q^{45} + 24 q^{47} - 792 q^{55} + 1288 q^{57} + 4980 q^{59} + 7748 q^{63} - 696 q^{65} - 612 q^{67} - 3080 q^{69} - 6456 q^{75} - 16272 q^{77} + 640 q^{81} + 2820 q^{83} - 1656 q^{85} + 6604 q^{87} + 2844 q^{93} + 3540 q^{95} - 1944 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)