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Properties

Label 432.4.l
Level $432$
Weight $4$
Character orbit 432.l
Rep. character $\chi_{432}(107,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 432.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(432, [\chi])\).

Total New Old
Modular forms 444 192 252
Cusp forms 420 192 228
Eisenstein series 24 0 24

Trace form

\( 192 q + O(q^{10}) \) \( 192 q + 60 q^{10} + 612 q^{16} + 24 q^{19} - 36 q^{22} - 36 q^{28} + 492 q^{34} + 636 q^{40} - 432 q^{43} + 816 q^{46} + 9408 q^{49} + 324 q^{52} + 288 q^{55} - 4560 q^{58} - 912 q^{61} - 1512 q^{64} + 3264 q^{67} + 6120 q^{70} + 1200 q^{76} - 600 q^{82} + 240 q^{85} - 11220 q^{88} + 1800 q^{91} + 5652 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(432, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)