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Properties

Label 693.6.cm
Level $693$
Weight $6$
Character orbit 693.cm
Rep. character $\chi_{693}(26,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1280$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 693.cm (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(693, [\chi])\).

Total New Old
Modular forms 3904 1280 2624
Cusp forms 3776 1280 2496
Eisenstein series 128 0 128

Trace form

\( 1280 q - 2560 q^{4} - 152 q^{7} + O(q^{10}) \) \( 1280 q - 2560 q^{4} - 152 q^{7} - 2976 q^{10} + 39288 q^{16} - 51176 q^{22} + 100528 q^{25} + 5640 q^{28} + 59796 q^{31} - 25016 q^{37} + 214272 q^{40} + 27536 q^{43} - 26472 q^{46} + 55772 q^{49} + 110232 q^{52} - 78688 q^{58} + 627568 q^{64} - 261328 q^{67} + 262280 q^{70} + 156696 q^{73} - 68448 q^{79} - 1169328 q^{82} + 959800 q^{85} + 176580 q^{88} + 824872 q^{91} + 1984968 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(693, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(693, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)