Properties

Label 819.2.fy
Level $819$
Weight $2$
Character orbit 819.fy
Rep. character $\chi_{819}(50,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $336$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fy (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(819, [\chi])\).

Total New Old
Modular forms 464 336 128
Cusp forms 432 336 96
Eisenstein series 32 0 32

Trace form

\( 336q - 12q^{6} + 36q^{8} + O(q^{10}) \) \( 336q - 12q^{6} + 36q^{8} - 12q^{11} + 4q^{15} + 168q^{16} - 4q^{18} - 4q^{21} + 8q^{24} - 96q^{26} + 24q^{27} - 120q^{30} - 72q^{32} + 36q^{33} + 72q^{38} + 8q^{39} - 48q^{41} - 76q^{45} + 24q^{48} - 24q^{50} - 36q^{52} + 72q^{54} + 32q^{57} + 36q^{58} - 72q^{59} + 4q^{60} + 36q^{62} - 8q^{63} - 72q^{65} - 20q^{66} - 48q^{71} - 176q^{72} - 60q^{75} - 124q^{78} - 12q^{79} - 96q^{80} - 20q^{81} - 156q^{83} - 12q^{84} - 108q^{85} - 24q^{87} + 60q^{89} - 72q^{92} + 20q^{93} + 96q^{94} + 88q^{96} - 96q^{97} + 108q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(819, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
819.2.fy.a \(336\) \(6.540\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(819, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(819, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)