Properties

Label 900.3.bc
Level $900$
Weight $3$
Character orbit 900.bc
Rep. character $\chi_{900}(157,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $144$
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.bc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 1512 144 1368
Cusp forms 1368 144 1224
Eisenstein series 144 0 144

Trace form

\( 144q + 2q^{3} + O(q^{10}) \) \( 144q + 2q^{3} - 24q^{11} - 36q^{17} - 104q^{21} + 12q^{23} - 46q^{27} + 14q^{33} + 84q^{37} - 144q^{41} + 78q^{47} + 248q^{51} + 312q^{53} + 338q^{57} + 192q^{61} + 242q^{63} + 78q^{67} + 264q^{71} + 240q^{77} + 1148q^{81} - 132q^{83} - 172q^{87} - 336q^{91} - 364q^{93} + 90q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)