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Properties

Label 3024.2.dx
Level $3024$
Weight $2$
Character orbit 3024.dx
Rep. character $\chi_{3024}(109,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1024$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.dx (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 2352 1024 1328
Cusp forms 2256 1024 1232
Eisenstein series 96 0 96

Trace form

\( 1024 q + O(q^{10}) \) \( 1024 q - 32 q^{16} - 24 q^{22} - 12 q^{28} - 32 q^{34} + 52 q^{40} - 12 q^{52} + 16 q^{58} + 48 q^{64} - 64 q^{67} - 192 q^{70} + 192 q^{76} - 20 q^{82} + 32 q^{88} + 24 q^{91} - 60 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)