Properties

Label 819.2.bm
Level $819$
Weight $2$
Character orbit 819.bm
Rep. character $\chi_{819}(478,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $90$
Newform subspaces $8$
Sturm bound $224$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(224\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

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

Total New Old
Modular forms 240 98 142
Cusp forms 208 90 118
Eisenstein series 32 8 24

Trace form

\( 90q - 90q^{4} + q^{7} + O(q^{10}) \) \( 90q - 90q^{4} + q^{7} + 9q^{10} + 9q^{11} - 8q^{13} + 14q^{14} + 94q^{16} + 14q^{17} - 12q^{19} + 30q^{20} + 6q^{22} + 14q^{23} + 35q^{25} + 20q^{26} + 11q^{28} + 4q^{29} + 9q^{31} + 11q^{35} - 32q^{38} - 24q^{40} - 3q^{41} + 12q^{44} - 36q^{47} + 11q^{49} + 78q^{50} + 63q^{52} + 7q^{53} - 16q^{55} - 27q^{56} + 57q^{58} - 40q^{61} + 2q^{62} - 104q^{64} - 14q^{65} + 12q^{67} - 26q^{68} - 18q^{70} - 51q^{71} + 9q^{73} - 42q^{74} + 30q^{76} - 48q^{77} + 16q^{79} + 30q^{80} + 20q^{82} - 51q^{85} + 54q^{86} - 5q^{88} + 9q^{91} - 74q^{92} - 18q^{94} + 50q^{95} - 30q^{97} - 60q^{98} + O(q^{100}) \)

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.bm.a \(2\) \(6.540\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-4\) \(q+(-1+2\zeta_{6})q^{2}-q^{4}+(-2+\zeta_{6})q^{5}+\cdots\)
819.2.bm.b \(2\) \(6.540\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(6\) \(5\) \(q+(1-2\zeta_{6})q^{2}-q^{4}+(4-2\zeta_{6})q^{5}+\cdots\)
819.2.bm.c \(2\) \(6.540\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) \(q+2q^{4}+(-3+2\zeta_{6})q^{7}+(-3+4\zeta_{6})q^{13}+\cdots\)
819.2.bm.d \(4\) \(6.540\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(0\) \(0\) \(-6\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{3})q^{4}+\cdots\)
819.2.bm.e \(12\) \(6.540\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(6\) \(-3\) \(q+(\beta _{1}+\beta _{3}+\beta _{6})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
819.2.bm.f \(12\) \(6.540\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(3\) \(-3\) \(q+\beta _{9}q^{2}+(-1-\beta _{2}-\beta _{4}+\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots\)
819.2.bm.g \(20\) \(6.540\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(-6\) \(2\) \(q+(\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{1})q^{4}+\beta _{7}q^{5}+\cdots\)
819.2.bm.h \(36\) \(6.540\) None \(0\) \(0\) \(0\) \(8\)

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

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