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Properties

Label 693.4.c
Level $693$
Weight $4$
Character orbit 693.c
Rep. character $\chi_{693}(307,\cdot)$
Character field $\Q$
Dimension $118$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 296 122 174
Cusp forms 280 118 162
Eisenstein series 16 4 12

Trace form

\( 118 q - 478 q^{4} - 4 q^{11} - 34 q^{14} + 1874 q^{16} + 506 q^{22} + 112 q^{23} - 2546 q^{25} - 284 q^{37} - 352 q^{44} + 638 q^{49} - 572 q^{53} + 978 q^{56} + 264 q^{58} - 13566 q^{64} + 280 q^{67} + 4252 q^{70}+ \cdots + 1672 q^{92}+O(q^{100}) \) 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

\( S_{4}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)