Properties

Label 432.6.l
Level $432$
Weight $6$
Character orbit 432.l
Rep. character $\chi_{432}(107,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $320$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 432.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(432, [\chi])\).

Total New Old
Modular forms 732 320 412
Cusp forms 708 320 388
Eisenstein series 24 0 24

Trace form

\( 320 q + O(q^{10}) \) \( 320 q - 100 q^{10} - 5468 q^{16} + 2360 q^{19} + 2236 q^{22} - 8292 q^{28} + 26124 q^{34} + 444 q^{40} + 656 q^{43} - 103504 q^{46} + 768320 q^{49} - 48444 q^{52} - 110048 q^{55} - 31824 q^{58} + 48080 q^{61} + 93720 q^{64} - 97856 q^{67} - 522072 q^{70} + 181680 q^{76} + 101800 q^{82} - 132400 q^{85} + 55596 q^{88} - 100056 q^{91} - 13068 q^{94} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

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