Properties

Label 690.3.l
Level $690$
Weight $3$
Character orbit 690.l
Rep. character $\chi_{690}(137,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
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.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 345 \)
Character field: \(\Q(i)\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 592 192 400
Cusp forms 560 192 368
Eisenstein series 32 0 32

Trace form

\( 192 q + 8 q^{3} - 16 q^{6} + O(q^{10}) \) \( 192 q + 8 q^{3} - 16 q^{6} - 16 q^{12} + 16 q^{13} - 768 q^{16} - 64 q^{18} - 16 q^{25} - 64 q^{27} - 32 q^{31} - 64 q^{36} - 16 q^{46} - 32 q^{48} - 32 q^{52} - 592 q^{55} - 96 q^{70} + 128 q^{72} + 608 q^{73} - 96 q^{75} + 96 q^{78} + 416 q^{81} - 256 q^{82} - 304 q^{85} + 304 q^{87} + 544 q^{93} + 64 q^{96} + O(q^{100}) \)

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

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