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Properties

Label 3024.2.er
Level $3024$
Weight $2$
Character orbit 3024.er
Rep. character $\chi_{3024}(253,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $576$
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.er (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
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 576 1776
Cusp forms 2256 576 1680
Eisenstein series 96 0 96

Trace form

\( 576 q + O(q^{10}) \) \( 576 q + 28 q^{20} - 64 q^{26} + 56 q^{38} - 48 q^{46} + 288 q^{49} - 52 q^{50} + 36 q^{58} + 24 q^{59} + 24 q^{62} + 72 q^{64} + 52 q^{68} + 28 q^{74} - 24 q^{76} + 304 q^{80} + 72 q^{82} + 124 q^{86} + 48 q^{88} - 76 q^{92} + 128 q^{95} + O(q^{100}) \)

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

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