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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
693.2.be.a 693.be 21.g $56$ $5.534$ None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$

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

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