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Properties

Label 690.3.p
Level $690$
Weight $3$
Character orbit 690.p
Rep. character $\chi_{690}(19,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $480$
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.p (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
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 480 2480
Cusp forms 2800 480 2320
Eisenstein series 160 0 160

Trace form

\( 480 q + 96 q^{4} + 144 q^{9} + O(q^{10}) \) \( 480 q + 96 q^{4} + 144 q^{9} - 192 q^{16} - 88 q^{20} + 168 q^{25} - 64 q^{26} + 152 q^{29} + 8 q^{31} - 56 q^{35} - 288 q^{36} - 216 q^{39} - 40 q^{41} + 160 q^{46} - 424 q^{49} - 96 q^{50} - 604 q^{55} + 256 q^{59} + 616 q^{61} + 384 q^{64} - 192 q^{69} + 672 q^{70} + 152 q^{71} - 144 q^{75} + 968 q^{79} - 432 q^{81} + 1148 q^{85} - 256 q^{94} - 12 q^{95} + 1320 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)