Properties

Label 819.2.n
Level $819$
Weight $2$
Character orbit 819.n
Rep. character $\chi_{819}(100,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $90$
Newform subspaces $7$
Sturm bound $224$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.n (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 7 \)
Sturm bound: \(224\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(11\)

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

\( 90q - q^{2} - 43q^{4} + 2q^{5} - 2q^{7} + 12q^{8} + O(q^{10}) \) \( 90q - q^{2} - 43q^{4} + 2q^{5} - 2q^{7} + 12q^{8} - 2q^{10} + 6q^{11} + 14q^{14} - 35q^{16} - 11q^{17} - 4q^{19} + 6q^{20} - 14q^{22} + 5q^{23} - 39q^{25} + 2q^{26} - 12q^{28} + 4q^{29} - 9q^{31} - 23q^{32} - 20q^{34} - 9q^{35} + 7q^{37} - 8q^{38} - 16q^{40} - 7q^{41} + 12q^{43} + 2q^{44} + 4q^{46} - 10q^{47} - 26q^{49} + 28q^{52} - 19q^{53} + 26q^{55} - 31q^{56} + 14q^{58} + 15q^{59} - 28q^{61} - 18q^{62} - 8q^{64} + 8q^{65} - 20q^{67} - 59q^{68} - 2q^{70} - 3q^{71} + 3q^{73} - 7q^{74} - 10q^{76} - 16q^{77} - 20q^{79} + 32q^{80} - 44q^{82} - 10q^{83} + 13q^{85} - 20q^{86} + 18q^{88} - 14q^{89} + 29q^{91} - 50q^{92} - 16q^{94} + 39q^{95} + 40q^{97} + 33q^{98} + O(q^{100}) \)

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.n.a \(2\) \(6.540\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) \(q+(2-2\zeta_{6})q^{4}+(3-\zeta_{6})q^{7}+(3-4\zeta_{6})q^{13}+\cdots\)
819.2.n.b \(2\) \(6.540\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) \(q+(2-2\zeta_{6})q^{4}+(3-\zeta_{6})q^{7}+6q^{11}+\cdots\)
819.2.n.c \(2\) \(6.540\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(3\) \(-5\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
819.2.n.d \(12\) \(6.540\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(0\) \(-1\) \(9\) \(q+(\beta _{1}+\beta _{5}-\beta _{11})q^{2}+(\beta _{6}-\beta _{7})q^{4}+\cdots\)
819.2.n.e \(16\) \(6.540\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(1\) \(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{5}-\beta _{9}+\beta _{14}+\cdots)q^{4}+\cdots\)
819.2.n.f \(20\) \(6.540\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(-9\) \(q+(-\beta _{1}-\beta _{4})q^{2}+(-\beta _{2}-2\beta _{7}-\beta _{16}+\cdots)q^{4}+\cdots\)
819.2.n.g \(36\) \(6.540\) None \(0\) \(0\) \(0\) \(-8\)

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

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