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Properties

Label 690.3.u
Level $690$
Weight $3$
Character orbit 690.u
Rep. character $\chi_{690}(17,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $1920$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.u (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 345 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(690, [\chi])\).

Total New Old
Modular forms 5920 1920 4000
Cusp forms 5600 1920 3680
Eisenstein series 320 0 320

Trace form

\( 1920 q - 8 q^{3} + 16 q^{6} + O(q^{10}) \) \( 1920 q - 8 q^{3} + 16 q^{6} + 16 q^{12} - 16 q^{13} + 768 q^{16} - 288 q^{18} + 16 q^{25} + 64 q^{27} + 32 q^{31} + 484 q^{33} + 64 q^{36} - 704 q^{37} + 16 q^{46} + 32 q^{48} + 32 q^{52} + 592 q^{55} + 1232 q^{61} + 352 q^{66} + 96 q^{70} - 128 q^{72} - 608 q^{73} - 608 q^{75} - 96 q^{78} - 2704 q^{81} + 256 q^{82} + 304 q^{85} - 304 q^{87} - 544 q^{93} - 64 q^{96} + 4488 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(690, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(690, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)