Properties

Label 819.2.do
Level $819$
Weight $2$
Character orbit 819.do
Rep. character $\chi_{819}(361,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $90$
Newform subspaces $8$
Sturm bound $224$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.do (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: \(2\)
Distinguishing \(T_p\): \(2\)

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

\( 90q + 3q^{2} + 45q^{4} - 4q^{7} + O(q^{10}) \) \( 90q + 3q^{2} + 45q^{4} - 4q^{7} - 18q^{10} - 8q^{13} + 14q^{14} - 47q^{16} - 7q^{17} + 30q^{20} + 6q^{22} - 7q^{23} + 35q^{25} - 10q^{26} - 2q^{28} + 4q^{29} - 9q^{31} - 9q^{32} - 13q^{35} - 15q^{37} - 32q^{38} - 24q^{40} - 3q^{41} - 12q^{44} + 54q^{46} + 36q^{47} + 2q^{49} + 78q^{50} - 72q^{52} + 7q^{53} - 16q^{55} + 3q^{56} + 27q^{59} + 80q^{61} + 2q^{62} - 104q^{64} - 14q^{65} + 13q^{68} + 18q^{70} - 51q^{71} - 9q^{73} + 21q^{74} + 30q^{76} - 48q^{77} + 16q^{79} - 40q^{82} - 51q^{85} - 54q^{86} + 10q^{88} + 12q^{89} - 19q^{91} - 74q^{92} + 36q^{94} - 25q^{95} - 30q^{97} + 75q^{98} + O(q^{100}) \)

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.do.a \(2\) \(6.540\) \(\Q(\sqrt{-3}) \) None \(-3\) \(0\) \(-6\) \(1\) \(q+(-2+\zeta_{6})q^{2}+(1-\zeta_{6})q^{4}+(-2+\cdots)q^{5}+\cdots\)
819.2.do.b \(2\) \(6.540\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-5\) \(q+(-2+2\zeta_{6})q^{4}+(-3+\zeta_{6})q^{7}+(-3+\cdots)q^{13}+\cdots\)
819.2.do.c \(2\) \(6.540\) \(\Q(\sqrt{-3}) \) None \(3\) \(0\) \(3\) \(-5\) \(q+(2-\zeta_{6})q^{2}+(1-\zeta_{6})q^{4}+(1+\zeta_{6})q^{5}+\cdots\)
819.2.do.d \(4\) \(6.540\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(-3\) \(0\) \(6\) \(0\) \(q+(-1+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-2\beta _{3})q^{4}+\cdots\)
819.2.do.e \(12\) \(6.540\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(-3\) \(3\) \(q+\beta _{10}q^{2}+(\beta _{1}+\beta _{4}-\beta _{7}+\beta _{11})q^{4}+\cdots\)
819.2.do.f \(12\) \(6.540\) 12.0.\(\cdots\).1 None \(3\) \(0\) \(-6\) \(3\) \(q+(\beta _{1}+\beta _{6}-\beta _{8})q^{2}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.do.g \(20\) \(6.540\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(3\) \(0\) \(6\) \(-5\) \(q-\beta _{3}q^{2}+(\beta _{11}+\beta _{17})q^{4}-\beta _{8}q^{5}+\cdots\)
819.2.do.h \(36\) \(6.540\) None \(0\) \(0\) \(0\) \(4\)

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

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