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Properties

Label 855.2.l
Level $855$
Weight $2$
Character orbit 855.l
Rep. character $\chi_{855}(391,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $160$
Newform subspaces $2$
Sturm bound $240$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(855, [\chi])\).

Total New Old
Modular forms 248 160 88
Cusp forms 232 160 72
Eisenstein series 16 0 16

Trace form

\( 160 q + 8 q^{2} - 4 q^{3} + 160 q^{4} - 4 q^{6} + 2 q^{7} + 24 q^{8} - 12 q^{9} + O(q^{10}) \) \( 160 q + 8 q^{2} - 4 q^{3} + 160 q^{4} - 4 q^{6} + 2 q^{7} + 24 q^{8} - 12 q^{9} - 2 q^{11} - 12 q^{12} - 4 q^{13} + 160 q^{16} + 12 q^{17} - 4 q^{18} + 10 q^{19} - 6 q^{22} + 4 q^{24} - 80 q^{25} - 16 q^{26} - 4 q^{27} + 8 q^{28} - 6 q^{29} + 16 q^{30} + 8 q^{31} + 56 q^{32} - 34 q^{33} + 18 q^{34} - 16 q^{36} - 4 q^{37} + 22 q^{38} - 14 q^{39} - 12 q^{40} - 6 q^{41} + 6 q^{42} - 40 q^{43} - 44 q^{44} + 4 q^{45} - 12 q^{46} + 24 q^{47} - 46 q^{48} - 78 q^{49} - 4 q^{50} - 14 q^{51} - 16 q^{52} - 32 q^{53} + 22 q^{54} + 40 q^{56} - 56 q^{57} - 4 q^{59} + 14 q^{61} - 100 q^{62} - 48 q^{63} + 184 q^{64} - 16 q^{65} + 12 q^{66} - 16 q^{67} + 28 q^{68} - 20 q^{69} + 16 q^{71} + 104 q^{72} - 4 q^{73} + 2 q^{75} + 28 q^{76} + 20 q^{77} - 60 q^{78} - 4 q^{79} + 8 q^{80} - 28 q^{81} - 6 q^{82} + 6 q^{83} + 2 q^{84} + 28 q^{86} - 40 q^{87} - 18 q^{88} - 36 q^{89} - 28 q^{90} - 20 q^{91} - 192 q^{92} + 4 q^{95} - 108 q^{96} + 44 q^{97} + 10 q^{98} + 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(855, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
855.2.l.a 855.l 171.h $80$ $6.827$ None \(4\) \(-2\) \(-40\) \(1\) $\mathrm{SU}(2)[C_{3}]$
855.2.l.b 855.l 171.h $80$ $6.827$ None \(4\) \(-2\) \(40\) \(1\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(855, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(855, [\chi]) \cong \)