Properties

Label 693.2.bq
Level $693$
Weight $2$
Character orbit 693.bq
Rep. character $\chi_{693}(8,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $96$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 693.bq (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
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 416 96 320
Cusp forms 352 96 256
Eisenstein series 64 0 64

Trace form

\( 96 q - 24 q^{4} + O(q^{10}) \) \( 96 q - 24 q^{4} + 16 q^{16} + 12 q^{22} + 24 q^{25} + 20 q^{28} - 56 q^{31} + 32 q^{34} - 8 q^{37} + 80 q^{46} + 24 q^{49} + 80 q^{52} - 56 q^{55} - 48 q^{58} - 80 q^{61} + 32 q^{64} - 80 q^{67} - 40 q^{70} - 80 q^{73} - 40 q^{79} + 104 q^{82} + 120 q^{85} + 108 q^{88} + 8 q^{97} + O(q^{100}) \)

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.bq.a 693.bq 33.f $96$ $5.534$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

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

\( S_{2}^{\mathrm{old}}(693, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)