Properties

Label 690.3.s
Level $690$
Weight $3$
Character orbit 690.s
Rep. character $\chi_{690}(61,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $320$
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.s (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
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 320 2640
Cusp forms 2800 320 2480
Eisenstein series 160 0 160

Trace form

\( 320 q - 64 q^{4} - 96 q^{9} + O(q^{10}) \) \( 320 q - 64 q^{4} - 96 q^{9} + 48 q^{13} - 128 q^{16} - 440 q^{17} - 264 q^{19} + 80 q^{23} + 160 q^{25} + 352 q^{26} + 496 q^{29} + 544 q^{31} - 320 q^{35} - 192 q^{36} - 216 q^{39} - 424 q^{41} - 176 q^{43} - 160 q^{46} - 400 q^{47} + 344 q^{49} + 528 q^{51} + 96 q^{52} + 704 q^{53} + 440 q^{55} - 624 q^{58} + 496 q^{59} - 616 q^{61} - 160 q^{62} - 256 q^{64} - 88 q^{67} - 192 q^{69} - 104 q^{71} + 424 q^{73} - 240 q^{77} - 192 q^{78} - 88 q^{79} - 288 q^{81} + 1168 q^{82} - 704 q^{83} + 120 q^{85} - 144 q^{87} - 176 q^{89} + 160 q^{92} + 192 q^{93} - 96 q^{94} + 160 q^{95} + 528 q^{97} - 64 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)