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Properties

Label 690.3.t
Level $690$
Weight $3$
Character orbit 690.t
Rep. character $\chi_{690}(29,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $960$
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.t (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 345 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 2960 960 2000
Cusp forms 2800 960 1840
Eisenstein series 160 0 160

Trace form

\( 960 q - 192 q^{4} + 8 q^{6} + 56 q^{9} + O(q^{10}) \) \( 960 q - 192 q^{4} + 8 q^{6} + 56 q^{9} - 158 q^{15} - 384 q^{16} - 80 q^{19} + 40 q^{21} + 16 q^{24} + 288 q^{30} + 224 q^{31} - 32 q^{34} + 112 q^{36} - 144 q^{39} + 44 q^{45} - 136 q^{46} + 768 q^{49} - 112 q^{51} + 252 q^{54} + 12 q^{55} + 168 q^{60} - 696 q^{61} - 768 q^{64} - 144 q^{66} - 152 q^{69} - 208 q^{70} - 718 q^{75} - 160 q^{76} - 840 q^{79} - 88 q^{81} - 272 q^{84} - 908 q^{85} - 288 q^{90} + 64 q^{91} + 240 q^{94} + 32 q^{96} - 840 q^{99} + O(q^{100}) \)

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

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