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Properties

Label 693.4.bz
Level $693$
Weight $4$
Character orbit 693.bz
Rep. character $\chi_{693}(148,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1728$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 693.bz (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(693, [\chi])\).

Total New Old
Modular forms 2336 1728 608
Cusp forms 2272 1728 544
Eisenstein series 64 0 64

Trace form

\( 1728 q - 8 q^{2} + 864 q^{4} - 8 q^{5} - 60 q^{6} + 192 q^{8} - 124 q^{9} - 46 q^{11} + 160 q^{12} - 188 q^{15} + 3456 q^{16} + 456 q^{17} + 552 q^{18} + 540 q^{19} - 128 q^{20} + 112 q^{21} + 36 q^{22}+ \cdots - 4492 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(693, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(693, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)