Properties

Label 690.3.k
Level $690$
Weight $3$
Character orbit 690.k
Rep. character $\chi_{690}(277,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $2$
Sturm bound $432$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(432\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 592 88 504
Cusp forms 560 88 472
Eisenstein series 32 0 32

Trace form

\( 88q - 8q^{2} - 16q^{5} - 16q^{7} + 16q^{8} + O(q^{10}) \) \( 88q - 8q^{2} - 16q^{5} - 16q^{7} + 16q^{8} - 8q^{10} - 8q^{13} + 48q^{15} - 352q^{16} + 24q^{17} - 24q^{18} - 16q^{20} - 96q^{21} + 64q^{22} + 24q^{25} + 80q^{26} + 32q^{28} + 176q^{31} + 32q^{32} - 48q^{33} + 48q^{35} + 528q^{36} + 88q^{37} - 16q^{40} - 208q^{41} - 96q^{42} + 24q^{45} - 368q^{47} - 120q^{50} - 16q^{52} + 152q^{53} - 416q^{55} + 96q^{57} - 128q^{58} + 64q^{61} + 128q^{62} - 48q^{63} + 600q^{65} - 32q^{67} - 48q^{68} + 128q^{70} - 144q^{71} - 48q^{72} + 520q^{73} - 288q^{75} + 64q^{76} + 176q^{77} - 96q^{78} + 64q^{80} - 792q^{81} - 128q^{82} - 576q^{83} - 296q^{85} - 192q^{86} + 144q^{87} - 128q^{88} + 24q^{90} + 288q^{91} + 480q^{95} + 504q^{97} + 760q^{98} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
690.3.k.a \(40\) \(18.801\) None \(40\) \(0\) \(-8\) \(-8\)
690.3.k.b \(48\) \(18.801\) None \(-48\) \(0\) \(-8\) \(-8\)

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

\( S_{3}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)