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Properties

Label 819.2.m
Level $819$
Weight $2$
Character orbit 819.m
Rep. character $\chi_{819}(274,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $144$
Newform subspaces $6$
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.m (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(224\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 232 144 88
Cusp forms 216 144 72
Eisenstein series 16 0 16

Trace form

\( 144 q + 4 q^{2} + 8 q^{3} - 72 q^{4} - 4 q^{5} + 4 q^{6} - 24 q^{8} + 16 q^{9} + O(q^{10}) \) \( 144 q + 4 q^{2} + 8 q^{3} - 72 q^{4} - 4 q^{5} + 4 q^{6} - 24 q^{8} + 16 q^{9} + 12 q^{11} - 8 q^{12} + 8 q^{15} - 72 q^{16} + 24 q^{17} - 64 q^{18} + 24 q^{19} - 44 q^{20} - 12 q^{22} + 8 q^{23} + 40 q^{24} - 84 q^{25} - 40 q^{27} + 48 q^{30} - 12 q^{31} + 8 q^{32} - 52 q^{33} + 12 q^{34} + 16 q^{36} + 24 q^{37} + 52 q^{38} + 24 q^{40} - 28 q^{41} - 40 q^{42} - 12 q^{43} - 56 q^{44} + 44 q^{45} - 48 q^{46} - 16 q^{47} - 24 q^{48} - 72 q^{49} + 68 q^{50} - 44 q^{51} + 96 q^{53} + 28 q^{54} + 24 q^{55} - 12 q^{57} - 32 q^{59} + 104 q^{60} + 120 q^{62} + 8 q^{63} + 96 q^{64} + 16 q^{65} - 72 q^{66} - 24 q^{67} - 28 q^{68} + 76 q^{69} - 104 q^{71} + 148 q^{72} + 72 q^{73} - 44 q^{74} - 104 q^{75} - 12 q^{76} - 48 q^{80} - 8 q^{81} + 24 q^{82} - 8 q^{83} - 8 q^{86} - 8 q^{87} - 12 q^{88} - 128 q^{89} - 140 q^{90} - 44 q^{92} - 60 q^{93} + 24 q^{94} - 56 q^{95} + 76 q^{96} - 48 q^{97} - 8 q^{98} + 68 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.m.a 819.m 9.c $2$ $6.540$ \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
819.2.m.b 819.m 9.c $6$ $6.540$ 6.0.954288.1 None \(0\) \(-1\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{3}+(2+2\beta _{2})q^{4}+\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots\)
819.2.m.c 819.m 9.c $30$ $6.540$ None \(4\) \(3\) \(13\) \(-15\) $\mathrm{SU}(2)[C_{3}]$
819.2.m.d 819.m 9.c $34$ $6.540$ None \(2\) \(-1\) \(7\) \(17\) $\mathrm{SU}(2)[C_{3}]$
819.2.m.e 819.m 9.c $36$ $6.540$ None \(-2\) \(2\) \(-15\) \(-18\) $\mathrm{SU}(2)[C_{3}]$
819.2.m.f 819.m 9.c $36$ $6.540$ None \(-2\) \(2\) \(-7\) \(18\) $\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(819, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)