Properties

Label 3150.2.bj
Level 3150
Weight 2
Character orbit bj
Rep. character \(\chi_{3150}(2399,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 288
Sturm bound 1440

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bj (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

\( 288q + 288q^{4} + O(q^{10}) \) \( 288q + 288q^{4} - 24q^{11} - 12q^{14} + 288q^{16} - 20q^{21} + 12q^{29} + 36q^{39} + 12q^{41} - 24q^{44} - 12q^{46} - 12q^{49} - 16q^{51} - 12q^{56} + 288q^{64} + 84q^{69} + 24q^{79} - 8q^{81} - 20q^{84} + 72q^{89} + 72q^{99} + O(q^{100}) \)

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