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Properties

Label 828.2.ba
Level $828$
Weight $2$
Character orbit 828.ba
Rep. character $\chi_{828}(59,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $2800$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 828.ba (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 828 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(828, [\chi])\).

Total New Old
Modular forms 2960 2960 0
Cusp forms 2800 2800 0
Eisenstein series 160 160 0

Trace form

\( 2800 q - 27 q^{2} - 9 q^{4} - 54 q^{5} - 19 q^{6} - 36 q^{9} + O(q^{10}) \) \( 2800 q - 27 q^{2} - 9 q^{4} - 54 q^{5} - 19 q^{6} - 36 q^{9} - 28 q^{10} - 18 q^{12} - 18 q^{13} - 27 q^{14} - 9 q^{16} - 17 q^{18} - 27 q^{20} - 32 q^{21} - 28 q^{22} - 28 q^{24} - 142 q^{25} - 20 q^{28} - 78 q^{29} - 24 q^{30} - 27 q^{32} - 48 q^{33} - 25 q^{34} + 11 q^{36} - 72 q^{37} + 21 q^{38} + 35 q^{40} - 54 q^{41} - 28 q^{42} - 100 q^{45} - 56 q^{46} - 12 q^{48} - 134 q^{49} - 75 q^{50} - 34 q^{52} - 48 q^{54} + 15 q^{56} - 44 q^{57} - 10 q^{58} - 58 q^{60} - 18 q^{61} - 78 q^{64} - 6 q^{65} - 7 q^{66} - 6 q^{68} - 14 q^{69} - 10 q^{70} + 32 q^{72} - 72 q^{73} + 69 q^{74} - 5 q^{76} - 6 q^{77} - 143 q^{78} - 140 q^{81} - 46 q^{82} - 150 q^{84} - 38 q^{85} - 27 q^{86} + 7 q^{88} + 378 q^{90} - 57 q^{92} + 140 q^{93} + 36 q^{94} - 174 q^{96} - 18 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(828, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
828.2.ba.a 828.ba 828.aa $2800$ $6.612$ None \(-27\) \(0\) \(-54\) \(0\) $\mathrm{SU}(2)[C_{66}]$