Properties

Label 3150.2.dq
Level 3150
Weight 2
Character orbit dq
Rep. character \(\chi_{3150}(169,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 1440
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.dq (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 5824 1440 4384
Cusp forms 5696 1440 4256
Eisenstein series 128 0 128

Trace form

\( 1440q - 180q^{4} + 16q^{5} - 8q^{9} + O(q^{10}) \) \( 1440q - 180q^{4} + 16q^{5} - 8q^{9} + 8q^{11} - 20q^{12} - 8q^{14} + 20q^{15} + 180q^{16} + 4q^{20} - 48q^{25} - 24q^{29} + 16q^{30} - 24q^{31} - 16q^{36} + 12q^{39} + 16q^{44} + 144q^{45} + 100q^{47} + 40q^{48} + 720q^{49} - 4q^{50} + 40q^{51} + 48q^{54} - 24q^{55} + 8q^{56} - 12q^{59} + 16q^{60} + 20q^{63} + 360q^{64} + 152q^{65} + 60q^{67} - 68q^{69} - 80q^{71} + 160q^{74} + 40q^{78} + 8q^{80} - 16q^{81} - 24q^{85} + 40q^{86} + 300q^{87} - 160q^{89} - 60q^{90} + 60q^{92} + 12q^{95} + 88q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database