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Properties

Label 667.2.h
Level $667$
Weight $2$
Character orbit 667.h
Rep. character $\chi_{667}(59,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $560$
Newform subspaces $2$
Sturm bound $120$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 667 = 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 667.h (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(667, [\chi])\).

Total New Old
Modular forms 620 560 60
Cusp forms 580 560 20
Eisenstein series 40 0 40

Trace form

\( 560 q - 4 q^{3} - 64 q^{4} - 8 q^{5} - 8 q^{6} - 4 q^{7} - 60 q^{9} + O(q^{10}) \) \( 560 q - 4 q^{3} - 64 q^{4} - 8 q^{5} - 8 q^{6} - 4 q^{7} - 60 q^{9} - 12 q^{10} - 24 q^{11} - 16 q^{12} - 4 q^{13} - 16 q^{14} - 22 q^{15} - 80 q^{16} + 6 q^{17} + 56 q^{18} - 32 q^{19} + 36 q^{20} - 24 q^{21} - 36 q^{22} - 20 q^{23} - 24 q^{24} - 88 q^{25} - 44 q^{26} - 28 q^{27} + 72 q^{28} + 56 q^{30} - 10 q^{31} - 20 q^{32} + 2 q^{33} + 4 q^{34} + 16 q^{35} - 144 q^{36} + 56 q^{37} - 48 q^{38} - 32 q^{39} + 56 q^{40} - 8 q^{41} + 124 q^{42} - 28 q^{43} - 76 q^{44} - 92 q^{45} - 56 q^{46} + 44 q^{47} - 132 q^{48} - 116 q^{49} - 96 q^{50} - 56 q^{51} + 164 q^{52} - 32 q^{53} + 92 q^{54} - 72 q^{55} - 88 q^{56} + 16 q^{57} + 80 q^{59} + 44 q^{60} + 16 q^{61} - 84 q^{62} - 72 q^{63} + 16 q^{64} + 22 q^{65} - 124 q^{66} - 48 q^{67} + 80 q^{68} + 10 q^{69} + 48 q^{70} + 66 q^{71} + 60 q^{72} - 44 q^{73} - 88 q^{74} + 142 q^{75} + 150 q^{76} - 116 q^{77} - 12 q^{78} + 100 q^{79} + 80 q^{80} + 176 q^{81} - 40 q^{82} - 88 q^{83} + 132 q^{84} + 48 q^{85} + 6 q^{86} - 136 q^{88} - 76 q^{89} + 190 q^{90} - 96 q^{91} + 2 q^{92} - 224 q^{93} + 2 q^{94} - 74 q^{95} + 242 q^{96} - 10 q^{97} - 144 q^{98} - 14 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(667, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
667.2.h.a 667.h 23.c $280$ $5.326$ None \(0\) \(-2\) \(-8\) \(-10\) $\mathrm{SU}(2)[C_{11}]$
667.2.h.b 667.h 23.c $280$ $5.326$ None \(0\) \(-2\) \(0\) \(6\) $\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(667, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(667, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)