Properties

Label 3024.2.v
Level 3024
Weight 2
Character orbit v
Rep. character \(\chi_{3024}(323,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 384
Sturm bound 1152

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3024.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3024, [\chi])\).

Total New Old
Modular forms 1176 384 792
Cusp forms 1128 384 744
Eisenstein series 48 0 48

Trace form

\( 384q + O(q^{10}) \) \( 384q - 8q^{10} + 24q^{16} + 16q^{19} - 16q^{22} - 8q^{34} - 32q^{43} - 32q^{46} + 384q^{49} + 48q^{52} - 64q^{55} + 32q^{58} - 32q^{61} + 64q^{67} - 24q^{70} + 96q^{76} + 40q^{82} - 32q^{85} - 56q^{88} + 48q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3024, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3024, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database