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Properties

Label 869.2.u
Level $869$
Weight $2$
Character orbit 869.u
Rep. character $\chi_{869}(45,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $1584$
Newform subspaces $2$
Sturm bound $160$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 869 = 11 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 869.u (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 79 \)
Character field: \(\Q(\zeta_{39})\)
Newform subspaces: \( 2 \)
Sturm bound: \(160\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(869, [\chi])\).

Total New Old
Modular forms 1968 1584 384
Cusp forms 1872 1584 288
Eisenstein series 96 0 96

Trace form

\( 1584 q + 2 q^{3} + 72 q^{4} + 8 q^{6} + 2 q^{7} + 64 q^{9} + O(q^{10}) \) \( 1584 q + 2 q^{3} + 72 q^{4} + 8 q^{6} + 2 q^{7} + 64 q^{9} - 16 q^{10} - 48 q^{12} - 2 q^{13} - 126 q^{14} + 12 q^{15} + 84 q^{16} - 24 q^{17} - 114 q^{18} - 10 q^{19} + 28 q^{20} - 40 q^{21} - 12 q^{23} + 70 q^{25} - 10 q^{26} - 82 q^{27} - 10 q^{28} - 4 q^{29} - 22 q^{30} - 10 q^{31} - 20 q^{32} - 8 q^{33} - 16 q^{34} - 84 q^{35} + 88 q^{36} - 40 q^{37} - 60 q^{38} - 6 q^{39} + 48 q^{40} + 8 q^{41} - 66 q^{42} - 14 q^{43} - 6 q^{45} - 164 q^{46} - 8 q^{47} + 50 q^{48} + 52 q^{49} - 164 q^{50} - 28 q^{51} + 28 q^{52} + 20 q^{53} - 224 q^{54} - 282 q^{56} - 276 q^{57} - 68 q^{59} - 204 q^{60} - 56 q^{61} + 52 q^{62} - 154 q^{63} - 56 q^{64} + 28 q^{65} + 8 q^{66} + 2 q^{67} + 2 q^{68} - 28 q^{69} - 172 q^{70} + 24 q^{71} - 44 q^{73} + 32 q^{74} + 362 q^{75} + 192 q^{76} + 6 q^{77} + 360 q^{78} + 50 q^{79} - 316 q^{80} + 114 q^{81} + 206 q^{82} + 10 q^{83} + 298 q^{84} + 180 q^{85} + 198 q^{86} - 248 q^{87} + 60 q^{89} - 326 q^{90} + 96 q^{91} - 14 q^{92} + 82 q^{93} + 64 q^{94} + 22 q^{95} - 252 q^{96} - 114 q^{97} + 104 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(869, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
869.2.u.a 869.u 79.g $792$ $6.939$ None \(0\) \(-1\) \(0\) \(11\) $\mathrm{SU}(2)[C_{39}]$
869.2.u.b 869.u 79.g $792$ $6.939$ None \(0\) \(3\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{39}]$

Decomposition of \(S_{2}^{\mathrm{old}}(869, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(869, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 2}\)