Properties

Label 693.2.be
Level $693$
Weight $2$
Character orbit 693.be
Rep. character $\chi_{693}(89,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $56$
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.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 208 56 152
Cusp forms 176 56 120
Eisenstein series 32 0 32

Trace form

\( 56q + 32q^{4} - 4q^{7} + O(q^{10}) \) \( 56q + 32q^{4} - 4q^{7} - 40q^{16} - 12q^{19} - 36q^{25} + 48q^{28} + 12q^{31} - 12q^{37} - 120q^{40} - 8q^{43} - 56q^{46} + 20q^{49} + 72q^{52} + 32q^{58} + 24q^{61} - 64q^{64} + 44q^{67} + 40q^{70} + 12q^{73} - 20q^{79} + 168q^{82} - 16q^{85} + 24q^{88} - 92q^{91} - 96q^{94} + O(q^{100}) \)

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.be.a \(56\) \(5.534\) None \(0\) \(0\) \(0\) \(-4\)

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

\( S_{2}^{\mathrm{old}}(693, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)