Properties

Label 693.2.cq
Level $693$
Weight $2$
Character orbit 693.cq
Rep. character $\chi_{693}(29,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $576$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 693.cq (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(693, [\chi])\).

Total New Old
Modular forms 800 576 224
Cusp forms 736 576 160
Eisenstein series 64 0 64

Trace form

\( 576q - 6q^{3} + 72q^{4} - 6q^{5} + 10q^{6} + 2q^{9} + O(q^{10}) \) \( 576q - 6q^{3} + 72q^{4} - 6q^{5} + 10q^{6} + 2q^{9} - 12q^{11} + 56q^{12} - 6q^{15} + 72q^{16} - 20q^{18} + 60q^{19} + 24q^{20} + 6q^{22} - 30q^{24} - 78q^{25} - 90q^{29} - 60q^{30} + 6q^{31} + 2q^{33} + 12q^{34} - 26q^{36} - 12q^{37} - 120q^{38} - 110q^{39} + 24q^{45} + 24q^{47} + 12q^{48} - 72q^{49} + 30q^{51} - 60q^{57} - 120q^{59} + 32q^{60} - 144q^{64} + 20q^{66} - 36q^{67} - 390q^{68} - 26q^{69} - 150q^{72} - 32q^{75} - 232q^{78} + 106q^{81} - 36q^{82} + 90q^{83} + 80q^{84} + 102q^{86} + 114q^{88} + 200q^{90} - 36q^{91} + 228q^{92} + 66q^{93} + 120q^{95} + 320q^{96} - 60q^{97} - 158q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(693, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
693.2.cq.a \(576\) \(5.534\) None \(0\) \(-6\) \(-6\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(693, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(693, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)