Properties

Label 900.3.bo
Level $900$
Weight $3$
Character orbit 900.bo
Rep. character $\chi_{900}(29,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $480$
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.bo (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 2928 480 2448
Cusp forms 2832 480 2352
Eisenstein series 96 0 96

Trace form

\( 480q - 36q^{5} + 10q^{9} + O(q^{10}) \) \( 480q - 36q^{5} + 10q^{9} + 55q^{15} + 60q^{21} + 12q^{25} - 105q^{27} - 30q^{31} - 25q^{33} - 220q^{39} + 351q^{45} + 225q^{47} + 1680q^{49} - 170q^{51} - 42q^{55} - 135q^{59} + 5q^{63} + 225q^{65} - 195q^{67} - 80q^{69} + 12q^{75} + 360q^{77} - 120q^{79} - 390q^{81} - 48q^{85} + 525q^{87} - 324q^{95} - 430q^{99} + O(q^{100}) \)

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

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