Properties

Label 3150.2.bb
Level 3150
Weight 2
Character orbit bb
Rep. character \(\chi_{3150}(499,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 288
Sturm bound 1440

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Defining parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 1488 288 1200
Cusp forms 1392 288 1104
Eisenstein series 96 0 96

Trace form

\( 288q - 288q^{4} + 8q^{6} - 16q^{9} + O(q^{10}) \) \( 288q - 288q^{4} + 8q^{6} - 16q^{9} - 8q^{11} + 4q^{14} + 288q^{16} - 4q^{21} - 8q^{24} - 24q^{26} - 20q^{29} + 16q^{36} - 52q^{39} - 28q^{41} + 8q^{44} + 12q^{46} + 12q^{49} - 32q^{51} + 16q^{54} - 4q^{56} - 48q^{59} - 24q^{61} - 288q^{64} - 32q^{66} - 44q^{69} + 40q^{71} - 24q^{79} + 40q^{81} + 4q^{84} - 8q^{86} + 64q^{89} - 48q^{94} + 8q^{96} - 24q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database