Properties

Label 819.2.j
Level $819$
Weight $2$
Character orbit 819.j
Rep. character $\chi_{819}(235,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $10$
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 10 \)
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 80 160
Cusp forms 208 80 128
Eisenstein series 32 0 32

Trace form

\( 80 q - 2 q^{2} - 42 q^{4} + 6 q^{5} + 2 q^{7} + O(q^{10}) \) \( 80 q - 2 q^{2} - 42 q^{4} + 6 q^{5} + 2 q^{7} + 2 q^{10} - 2 q^{11} + 4 q^{13} - 6 q^{14} - 46 q^{16} - 8 q^{17} - 8 q^{19} - 16 q^{20} - 4 q^{22} - 4 q^{23} - 44 q^{25} + 6 q^{26} - 10 q^{28} + 32 q^{29} - 12 q^{31} + 8 q^{32} + 64 q^{34} - 16 q^{35} - 8 q^{37} + 6 q^{38} + 32 q^{40} + 4 q^{41} - 8 q^{43} - 38 q^{44} + 4 q^{46} + 38 q^{47} - 36 q^{49} - 8 q^{50} - 6 q^{52} + 8 q^{53} - 32 q^{55} + 20 q^{56} - 6 q^{58} + 18 q^{59} + 28 q^{61} + 36 q^{62} + 168 q^{64} - 2 q^{65} + 12 q^{67} - 50 q^{68} - 18 q^{70} + 12 q^{71} + 18 q^{73} - 22 q^{74} - 96 q^{76} - 8 q^{77} - 4 q^{79} - 14 q^{80} - 12 q^{82} - 4 q^{83} - 116 q^{85} - 22 q^{86} - 24 q^{88} - 4 q^{89} - 8 q^{91} + 124 q^{92} + 2 q^{94} - 20 q^{95} + 76 q^{97} - 82 q^{98} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
819.2.j.a 819.j 7.c $2$ $6.540$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(4\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
819.2.j.b 819.j 7.c $2$ $6.540$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
819.2.j.c 819.j 7.c $4$ $6.540$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-3\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(3\beta _{1}+3\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.j.d 819.j 7.c $6$ $6.540$ 6.0.64827.1 None \(-2\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{4}+\beta _{5})q^{2}+(-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.j.e 819.j 7.c $6$ $6.540$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{18}-\zeta_{18}^{2}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
819.2.j.f 819.j 7.c $8$ $6.540$ 8.0.4868829729.1 None \(-1\) \(0\) \(3\) \(9\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{3}-\beta _{6})q^{2}+(\beta _{3}+2\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
819.2.j.g 819.j 7.c $10$ $6.540$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{4}+\beta _{8})q^{2}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.j.h 819.j 7.c $10$ $6.540$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(0\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{7})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.j.i 819.j 7.c $12$ $6.540$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{6})q^{2}+(-1-\beta _{5}-\beta _{9})q^{4}+\cdots\)
819.2.j.j 819.j 7.c $20$ $6.540$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}+(-2-2\beta _{3}-\beta _{14})q^{4}-\beta _{10}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(819, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)