Properties

Label 3024.2.he
Level $3024$
Weight $2$
Character orbit 3024.he
Rep. character $\chi_{3024}(155,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $5184$
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.he (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 432 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 6960 5184 1776
Cusp forms 6864 5184 1680
Eisenstein series 96 0 96

Trace form

\( 5184 q + O(q^{10}) \) \( 5184 q - 36 q^{12} - 84 q^{20} - 312 q^{50} + 108 q^{58} - 72 q^{59} + 60 q^{60} - 12 q^{66} + 156 q^{68} + 84 q^{72} + 84 q^{74} - 168 q^{75} + 156 q^{78} + 60 q^{86} + 228 q^{92} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)