Properties

Label 693.2.bd
Level 693
Weight 2
Character orbit bd
Rep. character \(\chi_{693}(419,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 160
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.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{6})\)
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 200 160 40
Cusp forms 184 160 24
Eisenstein series 16 0 16

Trace form

\( 160q + 80q^{4} + 2q^{7} + 8q^{9} + O(q^{10}) \) \( 160q + 80q^{4} + 2q^{7} + 8q^{9} + 18q^{14} - 4q^{15} - 80q^{16} + 12q^{18} + 28q^{21} - 24q^{23} - 80q^{25} + 16q^{28} - 72q^{29} - 68q^{30} + 60q^{32} - 12q^{36} - 8q^{37} - 16q^{39} - 30q^{42} + 16q^{43} + 48q^{46} - 14q^{49} + 24q^{50} + 8q^{51} + 24q^{56} + 64q^{57} + 32q^{60} - 60q^{63} - 160q^{64} + 156q^{65} - 28q^{67} + 12q^{70} + 108q^{72} - 12q^{74} + 28q^{78} - 4q^{79} - 104q^{81} + 98q^{84} - 180q^{86} + 12q^{91} - 12q^{92} - 132q^{93} - 144q^{95} + O(q^{100}) \)

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.bd.a \(160\) \(5.534\) None \(0\) \(0\) \(0\) \(2\)

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

\( S_{2}^{\mathrm{old}}(693, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database