Properties

Label 819.2.et
Level $819$
Weight $2$
Character orbit 819.et
Rep. character $\chi_{819}(136,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $180$
Newform subspaces $5$
Sturm bound $224$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.et (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(224\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 480 196 284
Cusp forms 416 180 236
Eisenstein series 64 16 48

Trace form

\( 180q + 2q^{2} + 6q^{5} + 2q^{7} + 4q^{8} + O(q^{10}) \) \( 180q + 2q^{2} + 6q^{5} + 2q^{7} + 4q^{8} - 6q^{10} + 14q^{11} - 4q^{14} - 172q^{16} + 12q^{17} - 2q^{19} - 36q^{20} - 8q^{22} + 36q^{26} + 26q^{28} - 8q^{29} - 8q^{31} + 30q^{32} - 12q^{34} + 28q^{35} + 34q^{37} - 72q^{40} - 18q^{41} - 24q^{43} - 50q^{44} - 32q^{46} + 6q^{47} + 38q^{49} + 30q^{50} + 62q^{52} + 4q^{53} - 42q^{55} + 18q^{56} + 66q^{58} + 54q^{59} + 30q^{61} + 36q^{62} + 60q^{65} - 42q^{67} + 56q^{70} + 6q^{71} - 52q^{73} - 92q^{74} + 100q^{76} + 20q^{79} - 234q^{80} + 42q^{82} - 18q^{83} - 14q^{85} - 6q^{86} - 6q^{88} - 48q^{89} - 38q^{91} + 20q^{92} - 42q^{94} - 10q^{97} + 92q^{98} + O(q^{100}) \)

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.et.a \(4\) \(6.540\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-8\) \(q+2\zeta_{12}^{3}q^{4}+(-1-2\zeta_{12}^{2})q^{7}+(-4\zeta_{12}+\cdots)q^{13}+\cdots\)
819.2.et.b \(28\) \(6.540\) None \(2\) \(0\) \(6\) \(-6\)
819.2.et.c \(36\) \(6.540\) None \(0\) \(0\) \(0\) \(6\)
819.2.et.d \(40\) \(6.540\) None \(0\) \(0\) \(0\) \(-2\)
819.2.et.e \(72\) \(6.540\) None \(0\) \(0\) \(0\) \(12\)

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

\( S_{2}^{\mathrm{old}}(819, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)