Properties

Label 900.3.bv
Level $900$
Weight $3$
Character orbit 900.bv
Rep. character $\chi_{900}(13,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $960$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.bv (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(900, [\chi])\).

Total New Old
Modular forms 5856 960 4896
Cusp forms 5664 960 4704
Eisenstein series 192 0 192

Trace form

\( 960q + 2q^{3} + O(q^{10}) \) \( 960q + 2q^{3} - 22q^{15} - 36q^{17} + 12q^{23} - 24q^{25} - 46q^{27} + 14q^{33} - 72q^{35} + 84q^{37} + 400q^{39} + 210q^{45} + 78q^{47} + 312q^{53} - 132q^{55} - 302q^{57} + 150q^{59} - 868q^{63} - 768q^{65} + 78q^{67} - 350q^{69} + 120q^{71} + 354q^{75} - 140q^{81} + 1128q^{83} - 96q^{85} + 478q^{87} + 1500q^{89} - 174q^{93} + 168q^{95} + 90q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

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