↑

Properties

Label 693.2.cg
Level $693$
Weight $2$
Character orbit 693.cg
Rep. character $\chi_{693}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $304$
Newform subspaces $3$
Sturm bound $192$
Trace bound $4$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 693.cg (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 3 \)
Sturm bound: \(192\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 832 336 496
Cusp forms 704 304 400
Eisenstein series 128 32 96

Trace form

\( 304 q + 5 q^{2} - 41 q^{4} + 3 q^{5} - 5 q^{7} + 40 q^{8} + O(q^{10}) \) \( 304 q + 5 q^{2} - 41 q^{4} + 3 q^{5} - 5 q^{7} + 40 q^{8} + 3 q^{11} - 4 q^{14} + 13 q^{16} + 45 q^{17} - 15 q^{19} + 52 q^{22} + 14 q^{23} - 31 q^{25} - 51 q^{26} + 20 q^{28} - 27 q^{31} + 75 q^{35} + 7 q^{37} - 9 q^{38} - 105 q^{40} + 52 q^{44} - 20 q^{46} + 21 q^{47} + 23 q^{49} - 30 q^{50} - 15 q^{52} - q^{53} + 112 q^{56} - 6 q^{58} - 45 q^{59} - 30 q^{61} - 132 q^{64} - 36 q^{67} - 105 q^{68} + q^{70} + 12 q^{71} - 60 q^{73} - 85 q^{74} - 30 q^{79} - 153 q^{80} + 63 q^{82} - 190 q^{85} - 84 q^{86} - 21 q^{88} - 6 q^{89} - 20 q^{91} + 174 q^{92} - 15 q^{94} - 40 q^{95} + O(q^{100}) \)

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.cg.a 693.cg 77.n $48$ $5.534$ None \(5\) \(0\) \(15\) \(-5\) $\mathrm{SU}(2)[C_{30}]$
693.2.cg.b 693.cg 77.n $128$ $5.534$ None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{30}]$
693.2.cg.c 693.cg 77.n $128$ $5.534$ None \(0\) \(0\) \(-12\) \(-10\) $\mathrm{SU}(2)[C_{30}]$

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

\( S_{2}^{\mathrm{old}}(693, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)