Properties

Label 3150.2.ba
Level 3150
Weight 2
Character orbit ba
Rep. character \(\chi_{3150}(799,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 216
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 45 \)
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 216 1272
Cusp forms 1392 216 1176
Eisenstein series 96 0 96

Trace form

\( 216q + 108q^{4} - 24q^{9} + O(q^{10}) \) \( 216q + 108q^{4} - 24q^{9} + 16q^{11} - 8q^{14} - 108q^{16} - 8q^{21} - 8q^{29} - 24q^{31} - 24q^{36} + 16q^{39} + 32q^{41} + 32q^{44} + 108q^{49} + 64q^{51} + 36q^{54} + 8q^{56} + 84q^{59} - 216q^{64} - 20q^{66} - 80q^{69} + 64q^{71} - 72q^{74} - 24q^{79} + 72q^{81} - 16q^{84} + 28q^{86} + 160q^{89} - 48q^{91} - 12q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database