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Properties

Label 900.3.bd
Level $900$
Weight $3$
Character orbit 900.bd
Rep. character $\chi_{900}(407,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $848$
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.bd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 180 \)
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 1488 880 608
Cusp forms 1392 848 544
Eisenstein series 96 32 64

Trace form

\( 848 q + 6 q^{2} - 8 q^{6} + O(q^{10}) \) \( 848 q + 6 q^{2} - 8 q^{6} - 14 q^{12} + 4 q^{13} - 4 q^{16} + 24 q^{18} - 48 q^{21} - 14 q^{22} - 56 q^{28} + 186 q^{32} - 28 q^{33} + 152 q^{36} + 16 q^{37} + 30 q^{38} - 24 q^{41} - 178 q^{42} - 352 q^{46} + 202 q^{48} + 66 q^{52} + 492 q^{56} + 48 q^{57} - 14 q^{58} - 8 q^{61} + 576 q^{66} + 102 q^{68} - 210 q^{72} + 16 q^{73} - 380 q^{76} + 12 q^{77} + 510 q^{78} + 144 q^{81} + 24 q^{82} + 636 q^{86} + 106 q^{88} - 336 q^{92} - 628 q^{93} + 256 q^{96} + 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)