Properties

Label 252.9.q
Level $252$
Weight $9$
Character orbit 252.q
Rep. character $\chi_{252}(143,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $256$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 252.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(252, [\chi])\).

Total New Old
Modular forms 784 256 528
Cusp forms 752 256 496
Eisenstein series 32 0 32

Trace form

\( 256 q + O(q^{10}) \) \( 256 q - 55676 q^{16} - 447872 q^{22} - 9362624 q^{25} + 3693340 q^{28} - 4288960 q^{37} - 14414340 q^{40} + 6048816 q^{46} + 18969088 q^{49} + 34461108 q^{52} + 13029596 q^{58} + 24843480 q^{64} + 84129300 q^{70} + 282911040 q^{73} + 101638356 q^{82} + 139238144 q^{85} + 27558404 q^{88} + 237745260 q^{94} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

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

Decomposition of \(S_{9}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)